Finite Group Databasebeta

← C3×#70542 #11794330

Subgroups — C3×#70542 #11794330

Order 1152.

513 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#424C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#819C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic
6C3×#4995C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#70542C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×C4⋊C8—22no—
18C3×#823—22no—
19C3×#821—22no—
20C3×#819—22no—
21C3×#809—21no—
22C3×#809—21no—
23C3×#808—21no—
24C3×#807—21no—
25C2×C3×#108—31no—
26C3×#428—31no—
27C3×#424—21no—
28C3×#424D311yescharacteristic, complemented
29C3×#424C2×C311yescharacteristic, complemented
30C3×#418—31no—
31C2×C3×#102—31no—
32C2×C3×#100—31no—
33C2×#823C2×C311yescharacteristic
34C2×#821C2×C311yescharacteristic
35C2×#819C2×C311yescharacteristic, complemented
36#5001C2×C311yescharacteristic
37#4995C2×C311yescharacteristic, complemented
38C3×#343—31no—
39#4554C2×C311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
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—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8D412yes—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#2063—31noSylow
68C22×C3×D4—31no—
69C22×D12C22×C311yescharacteristic
70C2×C3×M16—21no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C22×C311yescharacteristic
75C22×C3×C8—21no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C22×C311yescharacteristic
78C3×#117—21no—
79C3×#117C2×D311yescharacteristic
80C3×#117C22×C311yescharacteristic
81C2×C3×C4⋊C4—31no—
82C2×C4⋊Dic3C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88C3×C4⋊C8—24no—
89C3×C4⋊C8—22no—
90C3×C4⋊C8—22no—
91C3×#102—62no—
92C3×#102—61no—
93C3×#102—61no—
94C3×#100—62no—
95#823—22no—
96#821—22no—
97#819—22no—
98#809—21no—
99#809—21no—
100#808—21no—
101#807—21no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—81no—
107C22×C3×D3—81no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×Q811yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3×Dic3—41no—
117C2×C3×Dic3—81no—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C32×C8—22no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—41no—
126C2×#108—31no—
127#428—31no—
128#424C3×D311yescharacteristic, complemented
129#418—31no—
130C2×#102—31no—
131C2×#100—31no—
132#343—31no—
133C24×C3—61no—
134C23×D3—21no—
135C2×C3×D4—32no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C22×Dic3—21no—
146C2×D12—21no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12C3×Q812yes—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—21no—
155C3×M16—21no—
156C3×M16—32no—
157C3×M16—41no—
158C3×M16—41no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—22no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—22no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8#6712yes—
175C2×C3×C8C3×D412yes—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4D1211yescharacteristic
181C3×C4⋊C4D1211yescharacteristic
182C3×C4⋊C4C3×D411yescharacteristic
183C3×C4⋊C4C3×D411yescharacteristic
184C3×C22⋊C4—22no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C42—22no—
188C3×C42—21no—
189C3×C42—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192#208—21no—
193#208—21no—
194#208—21no—
195#208C3×D412yes—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C22×C32—21no—
199C22×C32—21no—
200C22×C32#12111yescharacteristic
201C22×C32C22⋊Q811yescharacteristic
202C22×C32#12611yescharacteristic
203C2×C3×D3—42no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C2×C3×D3—82no—
208C32×C4—41no—
209C32×C4—41no—
210C32×C4#12111yescharacteristic
211C32×C4#12111yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C3×Dic3—81no—
215C22×D4—31no—
216C2×M16—31no—
217C2×M16—31no—
218C2×M16C2×C3×D311yescharacteristic
219C22×C8C2×C3×D311yescharacteristic
220#117C2×C3×D311yescharacteristic
221C2×C4⋊C4—31no—
222#108—62no—
223#107—61no—
224#106—61no—
225C4⋊C8—22no—
226#102—62no—
227#102—61no—
228#102—61no—
229#100—62no—
230C23×C3—21no—
231C23×C3—62no—
232C23×C3—121no—
233C23×C3—121no—
234C23×C3—241no—
235C23×C3—241no—
236C23×C3#23511yescharacteristic
237C23×C3C3×#4111yescharacteristic
238C22×D3—22no—
239C22×D3—41no—
240C22×D3—41no—
241C22×D3—81no—
242C22×D3—81no—
243C3×D4—62no—
244C3×D4—62no—
245C3×D4—121no—
246C3×D4—121no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—121no—
260C2×C3×C4—241no—
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4D3×D411yescharacteristic
263C2×C3×C4#23711yescharacteristic
264C2×C3×C4D3×Q811yescharacteristic
265C2×C3×C4#23911yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270C2×C3×C4C2×C3×Q811yescharacteristic
271C2×C3×C4C3×#4111yescharacteristic
272C2×C3×C4C3×#4111yescharacteristic
273C2×Dic3—41no—
274C2×Dic3—81no—
275D12—22no—
276D12—22no—
277D12—41no—
278D12—41no—
279C3×C8—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—42no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32#39611yescharacteristic
292C2×C32#47111yescharacteristic
293C2×C32#47211yescharacteristic
294C3×D3—82no—
295C24—61no—
296C2×D4—32no—
297C2×D4—61no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C22×C4—61no—
303C22×C4C22×C3×D311yescharacteristic
304M16—21no—
305M16—21no—
306M16—32no—
307M16—61no—
308M16—61no—
309M16—61no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8C3×#6712yes—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4C3×D1211yescharacteristic
319C4⋊C4C3×D1211yescharacteristic
320C22⋊C4—21no—
321C42—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—122no—
332C22×C3—242no—
333C22×C3—242no—
334C22×C3—241no—
335C22×C3—241no—
336C22×C3#89611yescharacteristic
337C22×C3#89811yescharacteristic
338C22×C3#93011yescharacteristic
339C22×C3C3×#12111yescharacteristic
340C22×C3C3×C22⋊Q811yescharacteristic
341C22×C3C3×#12611yescharacteristic
342C2×D3—42no—
343C2×D3—82no—
344C2×D3—81no—
345C2×D3—81no—
346C2×D3—82no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—42no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—241no—
358C3×C4#89511yescharacteristic
359C3×C4#89711yescharacteristic
360C3×C4#93911yescharacteristic
361C3×C4#94611yescharacteristic
362C3×C4C3×#12111yescharacteristic
363C3×C4C3×#12111yescharacteristic
364C3×C4C3×C22⋊Q811yescharacteristic
365C3×C4C3×C22⋊Q811yescharacteristic
366Dic3—81no—
367C32#206311yescharacteristic, complemented, Sylow
368C23—62no—
369C23—121no—
370C23—121no—
371C23—241no—
372C23—241no—
373C23C3×#23511yescharacteristic
374D4—62no—
375D4—62no—
376D4—121no—
377D4—121no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—121no—
381C2×C4—241no—
382C2×C4C2×C3×D1211yescharacteristic
383C2×C4C3×D3×D411yescharacteristic
384C2×C4C3×#23711yescharacteristic
385C2×C4C3×D3×Q811yescharacteristic
386C2×C4C3×#23911yescharacteristic
387C2×C4C2×C3×#6711yescharacteristic
388C8—22no—
389C8—41no—
390C8—62no—
391C8—121no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—41no—
400C2×C3—41no—
401C2×C3—242no—
402C2×C3#499411yescharacteristic
403C2×C3#514111yescharacteristic
404C2×C3#514211yescharacteristic
405C2×C3C3×#39611yescharacteristic
406C2×C3C3×#47111yescharacteristic
407C2×C3C3×#47211yescharacteristic
408D3—82no—
409C22—21no—
410C22—21no—
411C22—122no—
412C22—242no—
413C22—242no—
414C22—241no—
415C22—241no—
416C22C3×#89611yescharacteristic
417C22C3×#89811yescharacteristic
418C22C3×#93011yescharacteristic
419C4—41no—
420C4—41no—
421C4—241no—
422C4C3×#89511yescharacteristic
423C4C3×#89711yescharacteristic
424C4C3×#93911yescharacteristic
425C4C3×#94611yescharacteristic
426C3—21no—
427C3#7054211yescharacteristic, direct product factor
428C3C3×#206311yescharacteristic, complemented
429C2—21no—
430C2—21no—
431C2—242no—
432C2C3×#499411yescharacteristic
433C2C3×#514111yescharacteristic
434C2C3×#514211yescharacteristic
subgroupG/H
centerC22×C3#930
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#424C2
socleC22×C32#121
prime radicalC22×C3×D12C22
hypercenterC3×#424D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#424

Complements

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

NH ≅ G/Ntype
1. C32×#424C2semidirect
4. C2×C3×#819C2semidirect
6. C3×#4995C2semidirect
7. C3×#4554C2semidirect
9. #70542C3direct (N × H)
28. C3×#424D3semidirect
29. C3×#424C2×C3semidirect
35. C2×#819C2×C3semidirect
37. #4995C2×C3semidirect
39. #4554C2×C3semidirect
128. #424C3×D3semidirect
367. C32#2063semidirect
427. C3#70542direct (N × H)
428. C3C3×#2063semidirect

Maximal subgroups

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

subgroupindex
C32×#4242
C2×C3×#8232
C2×C3×#8212
C2×C3×#8192
C3×#50012
C3×#49952
C3×#45542
C3×#20633
#705423