Finite Group Databasebeta

← C3×#68996 #11794336

Subgroups — C3×#68996 #11794336

Order 1152.

505 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5131C211yesmaximal, characteristic
2C2×C3×#823C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4C3×#5119C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C3×#4964C211yesmaximal, characteristic, complemented
7C32×#343C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#68996C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#823—22no—
18C3×#822—22no—
19C3×#821—21no—
20C3×#821—21no—
21C3×Dic3⋊C8—22no—
22C3×#809—22no—
23C3×#808—21no—
24C3×#807—21no—
25C2×C3×#108—31no—
26C3×#428—31no—
27C3×#424—31no—
28C3×#418—31no—
29C2×C3×#102—31no—
30C2×C3×#100—31no—
31#5131C2×C311yescharacteristic
32C2×#823C2×C311yescharacteristic
33C2×#822C2×C311yescharacteristic, complemented
34#5119C2×C311yescharacteristic, complemented
35C2×#809C2×C311yescharacteristic
36#4964C2×C311yescharacteristic, complemented
37C3×#343—21no—
38C3×#343D311yescharacteristic, complemented
39C3×#343C2×C311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12Q812yes—
49C32×M16—21no—
50C32×M16—21no—
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C3×#217—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4×Dic3—21no—
61C3×#208—21no—
62C3×#208D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#2063—31noSylow
68C22×C3×D4—31no—
69C22×D12C22×C311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C22×C3×C8—31no—
78C3×#117—31no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C22×C311yescharacteristic
82#926C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88C3×C4⋊C8—62no—
89C3×#102—62no—
90C3×#102—61no—
91C3×#102—61no—
92C3×#100—62no—
93#823—22no—
94#822—22no—
95#821—21no—
96#821—21no—
97Dic3⋊C8—22no—
98#809—22no—
99#808—21no—
100#807—21no—
101C23×C32#4111yescharacteristic
102C22×C3×D3—22no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—81no—
106C22×C3×D3—81no—
107C2×C32×C4—41no—
108C2×C32×C4—81no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×Q811yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C32×C8—41no—
122C32×C8—41no—
123C3×C3⋊C8—22no—
124C3×C3⋊C8—22no—
125C2×#108—31no—
126#428—31no—
127#424—31no—
128#418—31no—
129C2×#102—31no—
130C2×#100—31no—
131#343C3×D311yescharacteristic, complemented
132C24×C3—61no—
133C23×D3—21no—
134C2×C3×D4—32no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C23×C311yescharacteristic
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12C3×Q812yes—
152C3×M16—22no—
153C3×M16—22no—
154C3×M16—21no—
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—32no—
163C3×M16—41no—
164C3×M16—41no—
165C3×M16—61no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—32no—
171C2×C3×C8—41no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—31no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C42—61no—
186#217—21no—
187C4⋊Dic3C3×D411yescharacteristic
188C4⋊Dic3C3×D411yescharacteristic
189C4×Dic3—21no—
190#208—21no—
191#208C3×D412yes—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8C3×D412yes—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32#12111yescharacteristic
199C22×C32C22⋊Q811yescharacteristic
200C22×C32#12611yescharacteristic
201C2×C3×D3—42no—
202C2×C3×D3—82no—
203C2×C3×D3—81no—
204C2×C3×D3—81no—
205C2×C3×D3—82no—
206C32×C4—81no—
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C3×Dic3—41no—
212C3×Dic3—41no—
213C22×D4—31no—
214C2×M16—31no—
215C2×M16C2×C3×D311yescharacteristic
216C2×M16C2×C3×D311yescharacteristic
217C22×C8—31no—
218#117—31no—
219C2×C4⋊C4C2×C3×D311yescharacteristic
220#108—62no—
221#107—61no—
222#106—61no—
223C4⋊C8—62no—
224#102—62no—
225#102—61no—
226#102—61no—
227#100—62no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—121no—
231C23×C3—121no—
232C23×C3—241no—
233C23×C3—241no—
234C23×C3#23511yescharacteristic
235C23×C3C3×#4111yescharacteristic
236C22×D3—22no—
237C22×D3—41no—
238C22×D3—41no—
239C22×D3—81no—
240C22×D3—81no—
241C3×D4—62no—
242C3×D4—62no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—81no—
257C2×C3×C4—81no—
258C2×C3×C4—82no—
259C2×C3×C4#23511yescharacteristic
260C2×C3×C4#23511yescharacteristic
261C2×C3×C4D3×D411yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×Q811yescharacteristic
265C2×C3×C4C2×C3×D411yescharacteristic
266C2×C3×C4C2×C3×D411yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×Q811yescharacteristic
269C2×C3×C4C3×#4111yescharacteristic
270C2×C3×C4C3×#4111yescharacteristic
271C2×Dic3—21no—
272C2×Dic3—21no—
273D12—22no—
274D12—22no—
275D12—41no—
276D12—41no—
277C3×C8—42no—
278C3×C8—42no—
279C3×C8—41no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—41no—
283C3×C8—62no—
284C3×C8—62no—
285C3⋊C8—22no—
286C3⋊C8—22no—
287C2×C32—21no—
288C2×C32—21no—
289C2×C32#39611yescharacteristic
290C2×C32#47111yescharacteristic
291C2×C32#47211yescharacteristic
292C3×D3—82no—
293C24—61no—
294C2×D4—32no—
295C2×D4—61no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—61no—
300C22×C4—21no—
301C22×C4C22×C3×D311yescharacteristic
302M16—21no—
303M16—21no—
304M16—21no—
305M16—21no—
306M16—32no—
307M16—61no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—32no—
311C2×C8—61no—
312C2×C8—61no—
313C2×C8—61no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—31no—
317C4⋊C4—31no—
318C22⋊C4—61no—
319C42—61no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—122no—
330C22×C3—242no—
331C22×C3—242no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#87611yescharacteristic
335C22×C3#88411yescharacteristic
336C22×C3#89611yescharacteristic
337C22×C3C3×#12111yescharacteristic
338C22×C3C3×C22⋊Q811yescharacteristic
339C22×C3C3×#12611yescharacteristic
340C2×D3—42no—
341C2×D3—82no—
342C2×D3—81no—
343C2×D3—81no—
344C2×D3—82no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—82no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4#88411yescharacteristic
355C3×C4#88411yescharacteristic
356C3×C4#89611yescharacteristic
357C3×C4#89611yescharacteristic
358C3×C4C3×#12111yescharacteristic
359C3×C4C3×#12111yescharacteristic
360C3×C4C3×C22⋊Q811yescharacteristic
361C3×C4C3×C22⋊Q811yescharacteristic
362Dic3—41no—
363Dic3—41no—
364C32#206311yescharacteristic, complemented, Sylow
365C23—62no—
366C23—121no—
367C23—121no—
368C23—241no—
369C23—241no—
370C23C3×#23511yescharacteristic
371D4—62no—
372D4—62no—
373D4—121no—
374D4—121no—
375C2×C4—41no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—81no—
379C2×C4C3×#23511yescharacteristic
380C2×C4C3×#23511yescharacteristic
381C2×C4C3×D3×D411yescharacteristic
382C2×C4C3×D3×D411yescharacteristic
383C2×C4C3×D3×D411yescharacteristic
384C2×C4C3×D3×Q811yescharacteristic
385C8—41no—
386C8—41no—
387C8—62no—
388C8—62no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—242no—
399C2×C3#467611yescharacteristic
400C2×C3#474911yescharacteristic
401C2×C3#475411yescharacteristic
402C2×C3C3×#39611yescharacteristic
403C2×C3C3×#47111yescharacteristic
404C2×C3C3×#47211yescharacteristic
405D3—82no—
406C22—21no—
407C22—21no—
408C22—122no—
409C22—242no—
410C22—242no—
411C22—241no—
412C22—241no—
413C22C3×#87611yescharacteristic
414C22C3×#88411yescharacteristic
415C22C3×#89611yescharacteristic
416C4—81no—
417C4—121no—
418C4—121no—
419C4C3×#88411yescharacteristic
420C4C3×#88411yescharacteristic
421C4C3×#89611yescharacteristic
422C4C3×#89611yescharacteristic
423C3—21no—
424C3#6899611yescharacteristic, direct product factor
425C3C3×#206311yescharacteristic, complemented
426C2—21no—
427C2—21no—
428C2—242no—
429C2C3×#467611yescharacteristic
430C2C3×#474911yescharacteristic
431C2C3×#475411yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC3×#343D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
3. C2×C3×#822C2semidirect
4. C3×#5119C2semidirect
6. C3×#4964C2semidirect
7. C32×#343C2semidirect
9. #68996C3direct (N × H)
33. C2×#822C2×C3semidirect
34. #5119C2×C3semidirect
36. #4964C2×C3semidirect
38. C3×#343D3semidirect
39. C3×#343C2×C3semidirect
131. #343C3×D3semidirect
364. C32#2063semidirect
424. C3#68996direct (N × H)
425. C3C3×#2063semidirect

Maximal subgroups

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

subgroupindex
C3×#51312
C2×C3×#8232
C2×C3×#8222
C3×#51192
C2×C3×#8092
C3×#49642
C32×#3432
C3×#20633
#689963