Finite Group Databasebeta

← C3×#70264 #11793937

Subgroups — C3×#70264 #11793937

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#942C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic
5C2×C3×#819C211yesmaximal, characteristic, complemented
6C3×#4966C211yesmaximal, characteristic
7C3×#4530C211yesmaximal, characteristic, complemented
8C3×#2052—31nomaximal
9#70264C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#216—21no—
15C3×#942—22no—
16C3×#942—22no—
17C2×C3×#215—21no—
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C32×#103—22no—
22C3×#836—22no—
23C3×(C2×D3)⋊C8—22no—
24C3×#819—22no—
25C3×#810—21no—
26C3×#809—21no—
27C2×C3×#137—31no—
28C2×#942C2×C311yescharacteristic
29C2×C3×#108—31no—
30C3×#417—31no—
31C2×C3×#103—21no—
32C2×C3×#103D311yescharacteristic, complemented
33C2×C3×#103C2×C311yescharacteristic, complemented
34C2×C3×#101—31no—
35C3×#408—31no—
36C2×#836C2×C311yescharacteristic, complemented
37#5110C2×C311yescharacteristic
38C2×#819C2×C311yescharacteristic, complemented
39#4966C2×C311yescharacteristic
40C3×#343—31no—
41#4530C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8D412yes—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#216—24no—
65C3×#215—24no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2052—31noSylow
76C2×C3×#41—31no—
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C22×C311yescharacteristic
80C2×#235C22×C311yescharacteristic
81C3×#137—62no—
82C3×#137—62no—
83C2×C3×Q16—61no—
84C2×C3×SD16—61no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×M16—31no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94C2×#216—21no—
95#942—22no—
96#942—22no—
97C2×#215—21no—
98C2×#208C22×C311yescharacteristic
99C2×#208C22×C311yescharacteristic
100C2×#208C22×C311yescharacteristic
101C3×#108—62no—
102C3×#103—24no—
103C3×#103—22no—
104C3×#103—22no—
105C3×#103—61no—
106C3×#102—61no—
107C3×#101—62no—
108C3×C22⋊C8—62no—
109#836—22no—
110(C2×D3)⋊C8—22no—
111#819—22no—
112#810—21no—
113#809—21no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—81no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C3×#67—41no—
132C3×#67—41no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12—21no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6—21no—
140C32×C8—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C2×#137—31no—
145C2×#108—31no—
146#417—31no—
147C2×#103C3×D311yescharacteristic, complemented
148C2×#101—31no—
149#408—31no—
150#343—31no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—22no—
158C2×C3×Q8—22no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—22no—
168C2×C3×Q8—31no—
169C2×C3×Q8—41no—
170C2×C3×Q8—41no—
171C2×C3×Q8—41no—
172C2×C3×Q8D1212yes—
173C2×C3×Q8C3×D412yes—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—41no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C23×C311yescharacteristic
186C2×#67—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190#235—21no—
191C2×D12C3×D411yescharacteristic
192C2×C4×D3—21no—
193C2×Dic6C3×D411yescharacteristic
194C3×Q16—64no—
195C3×SD16—64no—
196C3×M16—32no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—22no—
207C2×C3×C8—41no—
208C2×C3×C8—41no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8#6712yes—
213C2×C3×C8C3×D412yes—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—41no—
220#216—24no—
221#215—24no—
222#208—21no—
223#208—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208C3×D412yes—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32#12111yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#12411yescharacteristic
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4—42no—
240C32×C4—81no—
241C32×C4#12011yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12311yescharacteristic
245C3×Dic3—41no—
246C2×#41—31no—
247C22×Q8C2×C3×D311yescharacteristic
248#137—62no—
249#137—62no—
250C2×Q16—61no—
251C2×SD16—61no—
252C2×M16—31no—
253C2×M16—31no—
254C2×M16—31no—
255C22×C8C2×C3×D311yescharacteristic
256C2×C4⋊C4C2×C3×D311yescharacteristic
257#108—62no—
258#103—22no—
259#103—61no—
260#102—61no—
261#101—62no—
262C22⋊C8—62no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23711yescharacteristic
266C23×C3C3×#4111yescharacteristic
267C22×D3—21no—
268C3×Q8—24no—
269C3×Q8—22no—
270C3×Q8—22no—
271C3×Q8—22no—
272C3×Q8—22no—
273C3×Q8—42no—
274C3×Q8—42no—
275C3×Q8—42no—
276C3×Q8—41no—
277C3×Q8—41no—
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—61no—
281C3×Q8—61no—
282C3×D4—61no—
283C3×D4—61no—
284C3×D4—121no—
285C3×D4—121no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—61no—
305C2×C3×C4—82no—
306C2×C3×C4—81no—
307C2×C3×C4—81no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4C2×D1211yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×D411yescharacteristic
319C2×C3×C4C2×C3×D411yescharacteristic
320C2×C3×C4C3×#4111yescharacteristic
321C2×C3×C4C3×#4111yescharacteristic
322#67—41no—
323#67—41no—
324C2×Dic3—21no—
325D12—21no—
326D12—21no—
327C4×D3—41no—
328C4×D3—41no—
329Dic6—21no—
330Dic6—21no—
331C3×C8—22no—
332C3×C8—22no—
333C3×C8—42no—
334C3×C8—62no—
335C3×C8—121no—
336C3×C8—121no—
337C3⋊C8—22no—
338C3⋊C8—41no—
339C3⋊C8—41no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32#39411yescharacteristic
343C2×C32#47111yescharacteristic
344C2×C32#47311yescharacteristic
345C3×D3—81no—
346#41—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—31no—
356C2×Q8C3×D1212yes—
357C2×D4—31no—
358C2×D4—61no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—61no—
362C22×C4C22×C3×D311yescharacteristic
363Q16—64no—
364SD16—64no—
365M16—32no—
366M16—61no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8C3×#6712yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3—121no—
391C22×C3#88511yescharacteristic
392C22×C3#88611yescharacteristic
393C22×C3#93811yescharacteristic
394C22×C3C3×#12111yescharacteristic
395C22×C3C3×#12311yescharacteristic
396C22×C3C3×#12411yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—44no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—82no—
408C3×C4—81no—
409C3×C4—81no—
410C3×C4—121no—
411C3×C4#88211yescharacteristic
412C3×C4#88311yescharacteristic
413C3×C4#93011yescharacteristic
414C3×C4#93911yescharacteristic
415C3×C4C3×#12011yescharacteristic
416C3×C4C3×#12111yescharacteristic
417C3×C4C3×#12111yescharacteristic
418C3×C4C3×#12311yescharacteristic
419Dic3—41no—
420C32#205211yescharacteristic, complemented, Sylow
421C23—61no—
422C23C3×#23711yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—41no—
426Q8—41no—
427Q8—61no—
428Q8—61no—
429D4—61no—
430D4—61no—
431D4—121no—
432D4—121no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—61no—
438C2×C4—81no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4C2×C3×D1211yescharacteristic
442C2×C4C3×#23511yescharacteristic
443C2×C4C3×D3×D411yescharacteristic
444C2×C4C3×D3×D411yescharacteristic
445C2×C4C3×#23711yescharacteristic
446C2×C4C2×C3×#6711yescharacteristic
447C8—22no—
448C8—62no—
449C8—121no—
450C8—121no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—241no—
461C2×C3#496111yescharacteristic
462C2×C3#517711yescharacteristic
463C2×C3#519211yescharacteristic
464C2×C3C3×#39411yescharacteristic
465C2×C3C3×#47111yescharacteristic
466C2×C3C3×#47311yescharacteristic
467D3—81no—
468C22—21no—
469C22—21no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22C3×#88511yescharacteristic
474C22C3×#88611yescharacteristic
475C22C3×#93811yescharacteristic
476C4—42no—
477C4—81no—
478C4—121no—
479C4C3×#88211yescharacteristic
480C4C3×#88311yescharacteristic
481C4C3×#93011yescharacteristic
482C4C3×#93911yescharacteristic
483C3—21no—
484C3#7026411yescharacteristic, direct product factor
485C3C3×#205211yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—241no—
489C2C3×#496111yescharacteristic
490C2C3×#517711yescharacteristic
491C2C3×#519211yescharacteristic
subgroupG/H
centerC22×C3#938
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC2×C3×#103D3
hypocenterC3C3×#2052
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C2×C3×#836C2semidirect
5. C2×C3×#819C2semidirect
7. C3×#4530C2semidirect
9. #70264C3direct (N × H)
32. C2×C3×#103D3semidirect
33. C2×C3×#103C2×C3semidirect
36. C2×#836C2×C3semidirect
38. C2×#819C2×C3semidirect
41. #4530C2×C3semidirect
147. C2×#103C3×D3semidirect
420. C32#2052semidirect
484. C3#70264direct (N × H)
485. C3C3×#2052semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9422
C2×C32×#1032
C2×C3×#8362
C3×#51102
C2×C3×#8192
C3×#49662
C3×#45302
C3×#20523
#702643