Finite Group Databasebeta

← C3×#68373 #11780637

Subgroups — C3×#68373 #11780637

Order 1152.

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

normal subgroups only

This group has 446 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×#5700C211yesmaximal, characteristic
2C3×#5064C211yesmaximal, characteristic, complemented
3C3×#4715C211yesmaximal, characteristic, complemented
4C3×#4714C211yesmaximal, characteristic, complemented
5C32×#330C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7C3×#4464C211yesmaximal, characteristic, complemented
8C3×#1661—31nomaximal
9#68373C311yesmaximal, characteristic, direct product factor
10C32×#125C2211yescharacteristic
11C2×C3×Dic12—21no—
12C2×C3×#204—21no—
13C3×#896—21no—
14C3×#896—21no—
15C3×#895—21no—
16C3×#895—21no—
17C3×#894—21no—
18C3×#894—21no—
19C3×#875C2211yescharacteristic
20C3×#875C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C32×#97C2211yescharacteristic
23C32×#97C2211yescharacteristic
24C3×#821—21no—
25C3×#816—21no—
26C3×#808—21no—
27C3×#807—21no—
28C3×#803C2211yescharacteristic
29C3×#562—31no—
30#5700C2×C311yescharacteristic
31C3×#501—31no—
32C3×#497—31no—
33C3×#489—31no—
34#5064C2×C311yescharacteristic, complemented
35#4715C2×C311yescharacteristic, complemented
36#4714C2×C311yescharacteristic, complemented
37C3×#330—21no—
38C3×#330D311yescharacteristic, complemented
39C3×#330C2×C311yescharacteristic, complemented
40C3×#329—31no—
41C3×#329—31no—
42#4464C2×C311yescharacteristic, complemented
43#4464C2×C311yescharacteristic, complemented
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×D12D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6D411yescharacteristic
52C2×C3×Dic6D411yescharacteristic
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4D411yescharacteristic
58C32×C4⋊C4D411yescharacteristic
59C32×C42C2311yescharacteristic
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71C3×Dic12—42no—
72C3×#204—42no—
73#1661—31noSylow
74C2×C3×Q16—61no—
75C2×C3×SD16—61no—
76C3×C4⋊Q8—31no—
77C3×#125—21no—
78C3×#125C2×D311yescharacteristic
79C3×#125C22×C311yescharacteristic
80C3×#124—31no—
81C3×#124—31no—
82C3×#123—61no—
83C3×#123—61no—
84C3×C22⋊Q8—61no—
85C3×C22⋊Q8—61no—
86C3×#121—61no—
87C3×#121—61no—
88C2×Dic12—21no—
89C2×#204—21no—
90#896—21no—
91#896—21no—
92#895—21no—
93#895—21no—
94#894—21no—
95#894—21no—
96#875C22×C311yescharacteristic
97#875C22×C311yescharacteristic
98#869C22×C311yescharacteristic
99C3×#107—61no—
100C3×#106—61no—
101C3×#103—61no—
102C3×#102—61no—
103C3×#97—21no—
104C3×#97—21no—
105C3×#97—31no—
106C3×#97C2×D311yescharacteristic
107C3×#97C2×D311yescharacteristic
108C3×#97C22×C311yescharacteristic
109C3×#97C22×C311yescharacteristic
110#821—21no—
111#816—21no—
112#808—21no—
113#807—21no—
114#803C22×C311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C3×D12—41no—
126C3×D12—41no—
127C3×D12—81no—
128C3×D12—81no—
129C3×C4×D3—81no—
130C3×C4×D3—81no—
131C3×Dic6—41no—
132C3×Dic6—41no—
133C3×Dic6—41no—
134C3×Dic6—41no—
135C32×C8—22no—
136C32×C8—41no—
137C3×C3⋊C8—22no—
138#562—31no—
139#501—31no—
140#497—31no—
141#489—31no—
142#330C3×D311yescharacteristic, complemented
143#329—31no—
144#329—31no—
145C2×C3×Q8—31no—
146C2×C3×Q8—31no—
147C2×C3×Q8—61no—
148C2×C3×D4—31no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12C3×D411yescharacteristic
157C2×D12C3×D411yescharacteristic
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×Dic6—21no—
161C2×Dic6C3×D411yescharacteristic
162C2×Dic6C3×D411yescharacteristic
163C3×Q16—122no—
164C3×SD16—122no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
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—41no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4D1211yescharacteristic
185C3×C4⋊C4D1211yescharacteristic
186C3×C4⋊C4C3×D411yescharacteristic
187C3×C4⋊C4C3×D411yescharacteristic
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C42—21no—
195C3×C42C22×D311yescharacteristic
196C3×C42C23×C311yescharacteristic
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207C2×C3⋊C8—21no—
208Dic12—42no—
209#204—42no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4—41no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C2×Q16—61no—
226C2×SD16—61no—
227C4⋊Q8—31no—
228#125C2×C3×D311yescharacteristic
229#124—31no—
230#124—31no—
231#123—61no—
232#123—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235#121—61no—
236#121—61no—
237#107—61no—
238#106—61no—
239#103—61no—
240#102—61no—
241#97—31no—
242#97C2×C3×D311yescharacteristic
243#97C2×C3×D311yescharacteristic
244C23×C3—61no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3—21no—
248C3×Q8—121no—
249C3×Q8—121no—
250C3×Q8—121no—
251C3×Q8—121no—
252C3×D4—121no—
253C3×D4—121no—
254C3×D4—241no—
255C3×D4—241no—
256C2×C3×C4—21no—
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—61no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4—241no—
269C2×C3×C4—241no—
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—41no—
279D12—41no—
280D12—41no—
281D12—81no—
282D12—81no—
283C4×D3—81no—
284C4×D3—81no—
285Dic6—41no—
286Dic6—41no—
287Dic6—41no—
288Dic6—41no—
289C3×C8—22no—
290C3×C8—22no—
291C3×C8—42no—
292C3×C8—41no—
293C3×C8—41no—
294C3×C8—42no—
295C3×C8—62no—
296C3⋊C8—22no—
297C2×C32#45311yescharacteristic
298C2×C32#45511yescharacteristic
299C2×C32#45611yescharacteristic
300C3×D3—81no—
301C3×D3—81no—
302C2×Q8—31no—
303C2×Q8—31no—
304C2×Q8—61no—
305C2×D4—31no—
306C2×D4—31no—
307C2×D4—61no—
308C2×D4—61no—
309C22×C4—61no—
310C22×C4—61no—
311Q16—122no—
312SD16—122no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—61no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4C3×D1211yescharacteristic
323C4⋊C4C3×D1211yescharacteristic
324C22⋊C4—61no—
325C22⋊C4—61no—
326C22⋊C4—61no—
327C22⋊C4—61no—
328C22⋊C4—61no—
329C22⋊C4—61no—
330C42C22×C3×D311yescharacteristic
331C22×C3—21no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3—121no—
337C22×C3—121no—
338C22×C3#88211yescharacteristic
339C22×C3C3×#12011yescharacteristic
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—81no—
360C3×C4—81no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—241no—
364Dic3—41no—
365Dic3—41no—
366Dic3—81no—
367C32#166111yescharacteristic, complemented, Sylow
368C23—61no—
369C23—61no—
370Q8—121no—
371Q8—121no—
372Q8—121no—
373Q8—121no—
374D4—121no—
375D4—121no—
376D4—241no—
377D4—241no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—121no—
383C2×C4—241no—
384C2×C4—241no—
385C2×C4C2×C3×D1211yescharacteristic
386C2×C4C3×D3×D411yescharacteristic
387C2×C4C3×D3×D411yescharacteristic
388C8—22no—
389C8—41no—
390C8—62no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—241no—
395C2×C3—241no—
396C2×C3#475211yescharacteristic
397C2×C3#482211yescharacteristic
398C2×C3#482511yescharacteristic
399C2×C3C3×#45311yescharacteristic
400C2×C3C3×#45511yescharacteristic
401C2×C3C3×#45611yescharacteristic
402D3—81no—
403D3—81no—
404C22—121no—
405C22—121no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22—121no—
410C22C3×#88211yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—121no—
417C4—121no—
418C4—241no—
419C3—21no—
420C3#6837311yescharacteristic, direct product factor
421C3C3×#166111yescharacteristic, complemented
422C2—241no—
423C2—241no—
424C2C3×#475211yescharacteristic
425C2C3×#482211yescharacteristic
426C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#330C2
socleC22×C32#120
prime radicalC3×#5700C2
hypercenterC3×#330D3
hypocenterC3C3×#1661
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#330

Complements

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

NH ≅ G/Ntype
2. C3×#5064C2semidirect
3. C3×#4715C2semidirect
4. C3×#4714C2semidirect
5. C32×#330C2semidirect
6. C3×#4464C2semidirect
7. C3×#4464C2semidirect
9. #68373C3direct (N × H)
34. #5064C2×C3semidirect
35. #4715C2×C3semidirect
36. #4714C2×C3semidirect
38. C3×#330D3semidirect
39. C3×#330C2×C3semidirect
42. #4464C2×C3semidirect
43. #4464C2×C3semidirect
142. #330C3×D3semidirect
367. C32#1661semidirect
420. C3#68373direct (N × H)
421. C3C3×#1661semidirect

Maximal subgroups

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

subgroupindex
C3×#57002
C3×#50642
C3×#47152
C3×#47142
C32×#3302
C3×#44642
C3×#16613
#683733