Finite Group Databasebeta

← C3×#69640 #11794640

Subgroups — C3×#69640 #11794640

Order 1152.

677 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#390C211yesmaximal, characteristic
2C2×C3×#832C212yesmaximal
3C3×#4935C211yesmaximal, characteristic, complemented
4C3×#4529C212yesmaximal, complemented
5C3×#4524C211yesmaximal, characteristic, complemented
6C3×#2071—31nomaximal
7#69640C311yesmaximal, characteristic, direct product factor
8C22×C32×D4C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C22⋊C4—21no—
11C2×C32×C22⋊C4—21no—
12C2×C32×C42C2211yescharacteristic
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3—21no—
15C2×C3×C4⋊Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C3×#832—24no—
18C2×C3×#102—32no—
19C3×#390—21no—
20C3×#390D311yescharacteristic
21C3×#390C2×C311yescharacteristic
22C3×#384—31no—
23C2×#832C2×C312yes—
24#4935C2×C311yescharacteristic, complemented
25C3×#340—32no—
26C3×#336—31no—
27#4529C2×C312yescomplemented
28#4524C2×C311yescharacteristic, complemented
29C24×C32—21no—
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C2×C32×D4—21no—
33C2×C32×D4D412yes—
34C22×C32×C4—21no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—22no—
39C32×C4⋊C4—22no—
40C32×C22⋊C4—42no—
41C32×C22⋊C4—42no—
42C32×C42—22no—
43C3×C4⋊Dic3—22no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—42no—
46C3×C4⋊Dic3—42no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50#2071—31noSylow
51C22×C3×D4—21no—
52C22×C3×D4C2×D311yescharacteristic
53C22×C3×D4C22×C311yescharacteristic
54C22×C3×C8—32no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C4⋊C4—61no—
58C2×C3×C4⋊C4—61no—
59C2×C3×C4⋊C4C2×D311yescharacteristic
60C2×C3×C4⋊C4C22×C311yescharacteristic
61C2×C3×C22⋊C4—22no—
62C2×C3×C22⋊C4—22no—
63C2×C3×C22⋊C4—21no—
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—21no—
67C2×C3×C42—21no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C22×C311yescharacteristic
70C2×C4⋊Dic3—21no—
71C2×C4⋊Dic3—21no—
72C2×C4⋊Dic3C22×C312yes—
73C22×C3⋊C8C22×C312yes—
74C3×#102—64no—
75#832—24no—
76C23×C32—22no—
77C23×C32—41no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32—41no—
81C23×C32—41no—
82C23×C32—41no—
83C23×C32C2×D411yescharacteristic
84C32×D4—24no—
85C32×D4—42no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4D812yes—
94C2×C32×C4SD1612yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C32×C4#4112yes—
98C2×C32×C4#4112yes—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C3×C3⋊C8—42no—
103C2×#102—32no—
104#390C3×D311yescharacteristic
105#384—31no—
106#340—32no—
107#336—31no—
108C24×C3—22no—
109C24×C3—21no—
110C24×C3—21no—
111C2×C3×D4—22no—
112C2×C3×D4—21no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—21no—
118C2×C3×D4—22no—
119C2×C3×D4—42no—
120C2×C3×D4—42no—
121C2×C3×D4D1212yes—
122C2×C3×D4C3×D412yes—
123C22×C3×C4—22no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—62no—
130C22×C3×C4#6711yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4C3×D411yescharacteristic
133C22×C3×C4C3×D411yescharacteristic
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C23×C311yescharacteristic
136C22×Dic3—22no—
137C2×C3×C8—62no—
138C2×C3×C8—62no—
139C2×C3×C8—62no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—42no—
143C3×C4⋊C4—62no—
144C3×C4⋊C4—62no—
145C3×C4⋊C4—122no—
146C3×C4⋊C4—122no—
147C3×C22⋊C4—44no—
148C3×C22⋊C4—44no—
149C3×C22⋊C4—42no—
150C3×C22⋊C4—42no—
151C3×C22⋊C4—42no—
152C3×C22⋊C4—42no—
153C3×C42—22no—
154C3×C42—22no—
155C3×C42—42no—
156C4⋊Dic3—22no—
157C4⋊Dic3—22no—
158C4⋊Dic3—42no—
159C4⋊Dic3—42no—
160C2×C3⋊C8—22no—
161C2×C3⋊C8—22no—
162C2×C3⋊C8—22no—
163C22×C32—42no—
164C22×C32—42no—
165C22×C32—42no—
166C22×C32—81no—
167C22×C32—81no—
168C22×C32—81no—
169C22×C32—81no—
170C22×C32#12111yescharacteristic
171C22×C32#12311yescharacteristic
172C22×C32#12411yescharacteristic
173C22×C32C2×D811yescharacteristic
174C22×C32C2×SD1611yescharacteristic
175C22×C32AGL(1,ℤ/8)11yescharacteristic
176C22×C32#13711yescharacteristic
177C32×C4—22no—
178C32×C4—22no—
179C32×C4—81no—
180C32×C4#12312yes—
181C32×C4#12612yes—
182C3×Dic3—82no—
183C22×D4C2×C3×D311yescharacteristic
184C22×C8—32no—
185C2×C4⋊C4—32no—
186C2×C4⋊C4—61no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4C2×C3×D311yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C42C2×C3×D311yescharacteristic
192#102—64no—
193C23×C3—24no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3—42no—
202C23×C3—42no—
203C23×C3—41no—
204C23×C3—41no—
205C23×C3—41no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—41no—
210C23×C3—41no—
211C23×C3—41no—
212C23×C3—41no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3C2×#6711yescharacteristic
216C23×C3C2×C3×D411yescharacteristic
217C3×D4—24no—
218C3×D4—24no—
219C3×D4—44no—
220C3×D4—44no—
221C3×D4—42no—
222C3×D4—42no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—122no—
251C2×C3×C4—122no—
252C2×C3×C4—122no—
253C2×C3×C4#21312yes—
254C2×C3×C4#21412yes—
255C2×C3×C4C3×D812yes—
256C2×C3×C4C3×SD1612yes—
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4#23511yescharacteristic
259C2×C3×C4#23712yes—
260C2×C3×C4#23712yes—
261C2×C3×C4C2×C3×D411yescharacteristic
262C2×C3×C4C3×#4111yescharacteristic
263C2×C3×C4C3×#4112yes—
264C2×C3×C4C3×#4112yes—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268C3×C8—122no—
269C3⋊C8—42no—
270C2×C32—82no—
271C2×C32#39711yescharacteristic
272C2×C32#45911yescharacteristic
273C2×C32#46111yescharacteristic
274C2×C32#48011yescharacteristic
275C2×C32#48111yescharacteristic
276C2×C32#48611yescharacteristic
277C2×C32#48911yescharacteristic
278C24—21no—
279C2×D4—21no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4C3×D1212yes—
283C22×C4—21no—
284C22×C4—62no—
285C22×C4C3×#6711yescharacteristic
286C22×C4C3×#6711yescharacteristic
287C22×C4C22×C3×D311yescharacteristic
288C2×C8—62no—
289C2×C8—62no—
290C2×C8—62no—
291C4⋊C4—22no—
292C4⋊C4—62no—
293C4⋊C4—62no—
294C4⋊C4—122no—
295C4⋊C4—122no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C42—22no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—44no—
307C22×C3—44no—
308C22×C3—44no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—42no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—82no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—81no—
326C22×C3—81no—
327C22×C3#93011yescharacteristic
328C22×C3C2×#21311yescharacteristic
329C22×C3C2×#21411yescharacteristic
330C22×C3#93511yescharacteristic
331C22×C3#93611yescharacteristic
332C22×C3#94911yescharacteristic
333C22×C3#95111yescharacteristic
334C22×C3C3×#12111yescharacteristic
335C22×C3C3×#12311yescharacteristic
336C22×C3C3×#12411yescharacteristic
337C22×C3C2×C3×D811yescharacteristic
338C22×C3C2×C3×SD1611yescharacteristic
339C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
340C22×C3C3×#13711yescharacteristic
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—42no—
348C3×C4—42no—
349C3×C4—82no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4—242no—
353C3×C4#87912yes—
354C3×C4#88612yes—
355C3×C4C3×#12312yes—
356C3×C4C3×#12612yes—
357Dic3—82no—
358C32#207111yescharacteristic, complemented, Sylow
359C23—22no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23C2×C3×#6711yescharacteristic
367D4—24no—
368D4—42no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—122no—
377C2×C4—122no—
378C2×C4—122no—
379C2×C4C3×#21312yes—
380C2×C4C3×#21412yes—
381C2×C4C2×C3×D1211yescharacteristic
382C2×C4C3×#23511yescharacteristic
383C2×C4C3×#23712yes—
384C2×C4C3×#23712yes—
385C8—122no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—84no—
394C2×C3—82no—
395C2×C3—82no—
396C2×C3#495311yescharacteristic
397C2×C3#501511yescharacteristic
398C2×C3#501911yescharacteristic
399C2×C3#503311yescharacteristic
400C2×C3#503411yescharacteristic
401C2×C3#505511yescharacteristic
402C2×C3#507011yescharacteristic
403C2×C3C3×#39711yescharacteristic
404C2×C3C3×#45911yescharacteristic
405C2×C3C3×#46111yescharacteristic
406C2×C3C3×#48011yescharacteristic
407C2×C3C3×#48111yescharacteristic
408C2×C3C3×#48611yescharacteristic
409C2×C3C3×#48911yescharacteristic
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22C3×#93011yescharacteristic
418C22C2×C3×#21311yescharacteristic
419C22C2×C3×#21411yescharacteristic
420C22C3×#93511yescharacteristic
421C22C3×#93611yescharacteristic
422C22C3×#94911yescharacteristic
423C22C3×#95111yescharacteristic
424C4—22no—
425C4—22no—
426C4—81no—
427C4—242no—
428C4C3×#87912yes—
429C4C3×#88612yes—
430C3—21no—
431C3#6964011yescharacteristic, direct product factor
432C3C3×#207111yescharacteristic, complemented
433C2—82no—
434C2C3×#495311yescharacteristic
435C2C3×#501511yescharacteristic
436C2C3×#501911yescharacteristic
437C2C3×#503311yescharacteristic
438C2C3×#503411yescharacteristic
439C2C3×#505511yescharacteristic
440C2C3×#507011yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC3×#390D3
hypocenterC3C3×#2071
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
3. C3×#4935C2semidirect
4. C3×#4529C2semidirect
5. C3×#4524C2semidirect
7. #69640C3direct (N × H)
24. #4935C2×C3semidirect
27. #4529C2×C3semidirect
28. #4524C2×C3semidirect
358. C32#2071semidirect
431. C3#69640direct (N × H)
432. C3C3×#2071semidirect

Maximal subgroups

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

subgroupindex
C32×#3902
C2×C3×#8322
C3×#49352
C3×#45292
C3×#45242
C3×#20713
#696403