Finite Group Databasebeta

← C3×#70317 #11794333

Subgroups — C3×#70317 #11794333

Order 1152.

551 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#418C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6C3×#4995C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2063—31nomaximal
9#70317C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#102—21no—
18C32×#102—21no—
19C3×#833—22no—
20C3×#832—22no—
21C3×#822—22no—
22C3×#808—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)—22no—
25C2×C3×#108—31no—
26C3×#428—31no—
27C3×#424—31no—
28C3×#418—21no—
29C3×#418D311yescharacteristic
30C3×#418C2×C311yescharacteristic
31C2×C3×#102—31no—
32C2×C3×#100—31no—
33C2×#833C2×C311yescharacteristic
34C2×#832C2×C311yescharacteristic
35C2×#822C2×C311yescharacteristic, complemented
36#4999C2×C311yescharacteristic, complemented
37#4995C2×C311yescharacteristic, complemented
38C3×#343—31no—
39#4554C2×C311yescharacteristic, complemented
40C24×C32—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4Q812yes—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C32×M16—21no—
50C32×M16—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4D411yescharacteristic
53C32×C4⋊C4D411yescharacteristic
54C32×C22⋊C4—21no—
55C32×C42—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208D412yes—
62C2×C3×C3⋊C8—21no—
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—21no—
69C22×C3×D4C2×D311yescharacteristic
70C22×C3×D4C22×C311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C22×C311yescharacteristic
76C22×C3×C8—31no—
77C3×#117—21no—
78C3×#117C2×D311yescharacteristic
79C3×#117C22×C311yescharacteristic
80C2×C3×C4⋊C4—31no—
81C2×C4⋊Dic3C22×C311yescharacteristic
82C2×#208C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#108—62no—
86C3×#107—61no—
87C3×#106—61no—
88C3×C4⋊C8—62no—
89C3×#102—22no—
90C3×#102—22no—
91C3×#102—21no—
92C3×#102—21no—
93C3×#102—21no—
94C3×#102—21no—
95C3×#102—62no—
96C3×#100—62no—
97#833—22no—
98#832—22no—
99#822—22no—
100#808—21no—
101#807—21no—
102C4⋊(C3⋊C8)—22no—
103C23×C32—22no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—81no—
107C23×C32—81no—
108C23×C32#4111yescharacteristic
109C32×D4—22no—
110C32×D4—22no—
111C32×D4—41no—
112C32×D4—41no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×Q811yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3×Dic3—41no—
122C2×C3×Dic3—81no—
123C32×C8—41no—
124C3×C3⋊C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127C2×#108—31no—
128#428—31no—
129#424—31no—
130#418C3×D311yescharacteristic
131C2×#102—31no—
132C2×#100—31no—
133#343—31no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—41no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—22no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4—41no—
153C2×C3×D4Dic612yes—
154C2×C3×D4C3×Q812yes—
155C22×C3×C4—21no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C23×C311yescharacteristic
159C22×Dic3—21no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—32no—
165C3×M16—41no—
166C3×M16—41no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—32no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4#6711yescharacteristic
183C3×C4⋊C4#6711yescharacteristic
184C3×C4⋊C4C3×D411yescharacteristic
185C3×C4⋊C4C3×D411yescharacteristic
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—41no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—41no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208C3×D412yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8C3×D412yes—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—42no—
206C22×C32—82no—
207C22×C32—82no—
208C22×C32—81no—
209C22×C32—81no—
210C22×C32#12111yescharacteristic
211C22×C32C22⋊Q811yescharacteristic
212C22×C32#12611yescharacteristic
213C32×C4—41no—
214C32×C4—41no—
215C32×C4#12111yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4C22⋊Q811yescharacteristic
218C32×C4C22⋊Q811yescharacteristic
219C3×Dic3—81no—
220C22×D4C2×C3×D311yescharacteristic
221C2×M16—31no—
222C2×M16—31no—
223C2×M16C2×C3×D311yescharacteristic
224C22×C8—31no—
225#117C2×C3×D311yescharacteristic
226C2×C4⋊C4—31no—
227#108—62no—
228#107—61no—
229#106—61no—
230C4⋊C8—62no—
231#102—21no—
232#102—21no—
233#102—62no—
234#100—62no—
235C23×C3—22no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—81no—
246C23×C3—81no—
247C23×C3—81no—
248C23×C3—81no—
249C23×C3—82no—
250C23×C3—82no—
251C23×C3#23711yescharacteristic
252C23×C3C3×#4111yescharacteristic
253C3×D4—24no—
254C3×D4—22no—
255C3×D4—22no—
256C3×D4—22no—
257C3×D4—22no—
258C3×D4—42no—
259C3×D4—42no—
260C3×D4—42no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—41no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—121no—
278C2×C3×C4—241no—
279C2×C3×C4C2×Dic611yescharacteristic
280C2×C3×C4#23511yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4#23711yescharacteristic
284C2×C3×C4C2×#6711yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×Q811yescharacteristic
289C2×C3×C4C3×#4111yescharacteristic
290C2×C3×C4C3×#4111yescharacteristic
291C2×Dic3—41no—
292C2×Dic3—81no—
293C3×C8—42no—
294C3×C8—41no—
295C3×C8—41no—
296C3×C8—62no—
297C3×C8—62no—
298C3×C8—121no—
299C3⋊C8—22no—
300C3⋊C8—22no—
301C3⋊C8—41no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32—82no—
305C2×C32#39611yescharacteristic
306C2×C32#47111yescharacteristic
307C2×C32#47211yescharacteristic
308C24—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4C3×Dic612yes—
315C22×C4—61no—
316C22×C4C22×C3×D311yescharacteristic
317M16—21no—
318M16—21no—
319M16—32no—
320M16—61no—
321M16—61no—
322M16—61no—
323C2×C8—21no—
324C2×C8—32no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4C3×#6711yescharacteristic
332C4⋊C4C3×#6711yescharacteristic
333C22⋊C4—21no—
334C42—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—82no—
348C22×C3—82no—
349C22×C3—82no—
350C22×C3—82no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—84no—
354C22×C3—84no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#87811yescharacteristic
360C22×C3#87911yescharacteristic
361C22×C3#93911yescharacteristic
362C22×C3C3×#12111yescharacteristic
363C22×C3C3×C22⋊Q811yescharacteristic
364C22×C3C3×#12611yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—81no—
374C3×C4—81no—
375C3×C4—241no—
376C3×C4#87811yescharacteristic
377C3×C4#88411yescharacteristic
378C3×C4#92411yescharacteristic
379C3×C4#93811yescharacteristic
380C3×C4C3×#12111yescharacteristic
381C3×C4C3×#12111yescharacteristic
382C3×C4C3×C22⋊Q811yescharacteristic
383C3×C4C3×C22⋊Q811yescharacteristic
384Dic3—81no—
385C32#206311yescharacteristic, complemented, Sylow
386C23—22no—
387C23—41no—
388C23—41no—
389C23—81no—
390C23—81no—
391C23C3×#23711yescharacteristic
392D4—22no—
393D4—22no—
394D4—41no—
395D4—41no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—121no—
399C2×C4—241no—
400C2×C4C2×C3×Dic611yescharacteristic
401C2×C4C3×#23511yescharacteristic
402C2×C4C3×D3×D411yescharacteristic
403C2×C4C3×D3×D411yescharacteristic
404C2×C4C3×#23711yescharacteristic
405C2×C4C2×C3×#6711yescharacteristic
406C8—41no—
407C8—62no—
408C8—62no—
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—84no—
420C2×C3—82no—
421C2×C3—82no—
422C2×C3#494811yescharacteristic
423C2×C3#519911yescharacteristic
424C2×C3#520011yescharacteristic
425C2×C3C3×#39611yescharacteristic
426C2×C3C3×#47111yescharacteristic
427C2×C3C3×#47211yescharacteristic
428C22—21no—
429C22—21no—
430C22—42no—
431C22—82no—
432C22—82no—
433C22—81no—
434C22—81no—
435C22C3×#87811yescharacteristic
436C22C3×#87911yescharacteristic
437C22C3×#93911yescharacteristic
438C4—41no—
439C4—41no—
440C4—241no—
441C4C3×#87811yescharacteristic
442C4C3×#88411yescharacteristic
443C4C3×#92411yescharacteristic
444C4C3×#93811yescharacteristic
445C3—21no—
446C3#7031711yescharacteristic, direct product factor
447C3C3×#206311yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—82no—
451C2C3×#494811yescharacteristic
452C2C3×#519911yescharacteristic
453C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#418C2
socleC22×C32#121
prime radicalC22×C32×D4C22
hypercenterC3×#418D3
hypocenterC3C3×#2063
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
4. C2×C3×#822C2semidirect
5. C3×#4999C2semidirect
6. C3×#4995C2semidirect
7. C3×#4554C2semidirect
9. #70317C3direct (N × H)
35. C2×#822C2×C3semidirect
36. #4999C2×C3semidirect
37. #4995C2×C3semidirect
39. #4554C2×C3semidirect
385. C32#2063semidirect
446. C3#70317direct (N × H)
447. C3C3×#2063semidirect

Maximal subgroups

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

subgroupindex
C32×#4182
C2×C3×#8332
C2×C3×#8322
C2×C3×#8222
C3×#49992
C3×#49952
C3×#45542
C3×#20633
#703173