Finite Group Databasebeta

← C3×#70349 #11788362

Subgroups — C3×#70349 #11788362

Order 1152.

683 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#942C211yesmaximal, characteristic
2C3×#5745C211yesmaximal, characteristic
3C32×#419C211yesmaximal, characteristic, complemented
4C2×C3×#836C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic
6C3×C3⋊#338C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8C3×#1902—31nomaximal
9#70349C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C3×#216C412yescomplemented
15C3×#942—22no—
16C3×#942—22no—
17C2×C3×#215C412yescomplemented
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#907—22no—
22C3×D3×M16—22no—
23C3×#901—22no—
24C32×#103—22no—
25C3×#836—22no—
26C3×#805—22no—
27C2×C3×#137—31no—
28C3×#568—31no—
29C2×#942C2×C311yescharacteristic
30#5745C2×C311yescharacteristic
31C3×#421—31no—
32C3×#419—21no—
33C3×#419D311yescharacteristic, complemented
34C3×#419C2×C311yescharacteristic, complemented
35C2×C3×#101—31no—
36C2×#836C2×C311yescharacteristic, complemented
37#5005C2×C311yescharacteristic
38C3×#344—31no—
39C3×#338—31no—
40C3⋊#338C2×C311yescharacteristic, complemented
41#4533C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235D412yes—
54C3×#235D412yes—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6C2×C411yescharacteristic
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8D412yes—
61C32×C4⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C42—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⋊C8C2×C412yes—
75C3×ΓL(1,𝔽25)—24no—
76C3×D3×C8—24no—
77#1902—31noSylow
78C2×C3×#41—31no—
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C22×C311yescharacteristic
82C2×#235C22×C311yescharacteristic
83C3×#137—62no—
84C3×#137—62no—
85C2×C3×Q16—32no—
86C2×C3×SD16—32no—
87C3×#131—62no—
88C3×#131—62no—
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C22×C311yescharacteristic
96C3×#117—21no—
97C3×#117C2×D311yescharacteristic
98C3×#117C22×C311yescharacteristic
99C2×#216C3×C412yescomplemented
100#942—22no—
101#942—22no—
102C2×#215C3×C412yescomplemented
103C2×#208C22×C311yescharacteristic
104C2×#208C22×C311yescharacteristic
105C2×#208C22×C311yescharacteristic
106#907—22no—
107D3×M16—22no—
108#901—22no—
109C3×#104—62no—
110C3×#103—24no—
111C3×#103—22no—
112C3×#103—22no—
113C3×#101—62no—
114#836—22no—
115#805—22no—
116C23×C32#4111yescharacteristic
117C22×C3×D3—21no—
118C32×Q8—22no—
119C32×Q8—22no—
120C32×Q8—41no—
121C32×Q8—41no—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—21no—
135C3×D12—21no—
136C3×D12C22⋊C412yes—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×Dic6—21no—
140C3×Dic6C22⋊C412yes—
141C32×C8—22no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C2×#137—31no—
146#568—31no—
147#421—31no—
148#419C3×D311yescharacteristic, complemented
149C2×#101—31no—
150#344—31no—
151#338—31no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—22no—
159C2×C3×Q8—22no—
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—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—31no—
170C2×C3×Q8—41no—
171C2×C3×Q8—41no—
172C2×C3×Q8—41no—
173C2×C3×Q8C4×D312yes—
174C2×C3×Q8C2×C3×C412yes—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C23×C311yescharacteristic
184C2×#67—21no—
185#235—21no—
186#235—21no—
187#235C3×D412yes—
188#235C3×D412yes—
189C2×D12C2×C3×C411yescharacteristic
190C2×C4×D3—21no—
191C2×Dic6C2×C3×C411yescharacteristic
192C3×Q16—64no—
193C3×SD16—64no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—32no—
199C3×M16—41no—
200C3×M16—41no—
201C3×M16—64no—
202C3×M16—61no—
203C3×M16—61no—
204C3×M16—61no—
205C3×M16—61no—
206C3×M16—61no—
207C2×C3×C8—22no—
208C2×C3×C8—32no—
209C2×C3×C8—64no—
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×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—41no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—41no—
223#216—24no—
224#215—24no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—21no—
230#208C3×D412yes—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8C2×C3×C412yes—
234ΓL(1,𝔽25)—24no—
235D3×C8—24no—
236C22×C32—41no—
237C22×C32C4×D411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12311yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—81no—
242C32×C4—42no—
243C32×C4—81no—
244C32×C4C2×C22⋊C411yescharacteristic
245C32×C4C4×D411yescharacteristic
246C32×C4#12011yescharacteristic
247C32×C4#12111yescharacteristic
248C3×Dic3—22no—
249C2×#41—31no—
250C22×Q8C2×C3×D311yescharacteristic
251#137—62no—
252#137—62no—
253C2×Q16—32no—
254C2×SD16—32no—
255#131—62no—
256#131—62no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—31no—
260C2×M16—62no—
261C2×M16C2×C3×D311yescharacteristic
262#117C2×C3×D311yescharacteristic
263#104—62no—
264#103—22no—
265#101—62no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3#23711yescharacteristic
269C23×C3C3×#4111yescharacteristic
270C22×D3—21no—
271C3×Q8—24no—
272C3×Q8—22no—
273C3×Q8—22no—
274C3×Q8—22no—
275C3×Q8—22no—
276C3×Q8—32no—
277C3×Q8—42no—
278C3×Q8—42no—
279C3×Q8—42no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×Q8—41no—
283C3×Q8—41no—
284C3×Q8—61no—
285C3×D4—32no—
286C3×D4—62no—
287C3×D4—62no—
288C3×D4—61no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—61no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C22×C3×C411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×D411yescharacteristic
319C2×C3×C4C2×C3×D411yescharacteristic
320C2×C3×C4C2×C3×D411yescharacteristic
321C2×C3×C4C3×#4111yescharacteristic
322#67—22no—
323#67—22no—
324C2×Dic3—21no—
325D12—21no—
326D12C3×C22⋊C412yes—
327C4×D3—22no—
328C4×D3—22no—
329Dic6—21no—
330Dic6C3×C22⋊C412yes—
331C3×C8—22no—
332C3×C8—22no—
333C3×C8—42no—
334C3×C8—62no—
335C3×C8—62no—
336C3×C8—121no—
337C3⋊C8—22no—
338C3⋊C8—22no—
339C3⋊C8—41no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32#38611yescharacteristic
344C3×D3—42no—
345#41—32no—
346#41—32no—
347#41—61no—
348#41—61no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—31no—
355C2×Q8C3×C4×D312yes—
356C2×D4—31no—
357C2×D4—61no—
358C22×C4—21no—
359C22×C4—61no—
360C22×C4C22×C3×D311yescharacteristic
361Q16—64no—
362SD16—64no—
363M16—21no—
364M16—21no—
365M16—32no—
366M16—64no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371M16—61no—
372C2×C8—32no—
373C2×C8—64no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8C3×#6712yes—
377C4⋊C4—21no—
378C22⋊C4—21no—
379C42—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—42no—
386C22×C3—62no—
387C22×C3—241no—
388C22×C3#67⋊C411yescharacteristic
389C22×C3#88311yescharacteristic
390C22×C3#93811yescharacteristic
391C22×C3C3×C4×D411yescharacteristic
392C22×C3C3×#12111yescharacteristic
393C22×C3C3×#12311yescharacteristic
394C2×D3—22no—
395C2×D3—81no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—44no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—62no—
404C3×C4—82no—
405C3×C4—81no—
406C3×C4—81no—
407C3×C4D3×C22⋊C411yescharacteristic
408C3×C4#88411yescharacteristic
409C3×C4C4×#6711yescharacteristic
410C3×C4#93711yescharacteristic
411C3×C4C2×C3×C22⋊C411yescharacteristic
412C3×C4C3×C4×D411yescharacteristic
413C3×C4C3×#12011yescharacteristic
414C3×C4C3×#12111yescharacteristic
415Dic3—22no—
416C32#190211yescharacteristic, complemented, Sylow
417C23—61no—
418C23C3×#23711yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—32no—
422Q8—41no—
423Q8—41no—
424Q8—61no—
425D4—32no—
426D4—62no—
427D4—62no—
428D4—61no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—61no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4C2×C3×C4×D311yescharacteristic
437C2×C4C3×#23511yescharacteristic
438C2×C4C3×D3×D411yescharacteristic
439C2×C4C3×D3×D411yescharacteristic
440C2×C4C3×D3×D411yescharacteristic
441C2×C4C2×C3×#6711yescharacteristic
442C8—22no—
443C8—62no—
444C8—62no—
445C8—121no—
446C2×C3—22no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—122no—
457C2×C3#495611yescharacteristic
458C2×C3C3×#38611yescharacteristic
459D3—42no—
460C22—41no—
461C22—62no—
462C22—241no—
463C22C3×#67⋊C411yescharacteristic
464C22C3×#88311yescharacteristic
465C22C3×#93811yescharacteristic
466C4—42no—
467C4—62no—
468C4—81no—
469C4C3×D3×C22⋊C411yescharacteristic
470C4C3×#88411yescharacteristic
471C4C3×C4×#6711yescharacteristic
472C4C3×#93711yescharacteristic
473C3—21no—
474C3#7034911yescharacteristic, direct product factor
475C3C3×#190211yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—21no—
479C2—122no—
480C2C3×#495611yescharacteristic
subgroupG/H
centerC2×C3#4956
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#419C2
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#419D3
hypocenterC3C3×#1902
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
3. C32×#419C2semidirect
4. C2×C3×#836C2semidirect
6. C3×C3⋊#338C2semidirect
7. C3×#4533C2semidirect
9. #70349C3direct (N × H)
14. C2×C3×#216C4semidirect
17. C2×C3×#215C4semidirect
33. C3×#419D3semidirect
34. C3×#419C2×C3semidirect
36. C2×#836C2×C3semidirect
40. C3⋊#338C2×C3semidirect
41. #4533C2×C3semidirect
99. C2×#216C3×C4semidirect
102. C2×#215C3×C4semidirect
148. #419C3×D3semidirect
416. C32#1902semidirect
474. C3#70349direct (N × H)
475. C3C3×#1902semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9422
C3×#57452
C32×#4192
C2×C3×#8362
C3×#50052
C3×C3⋊#3382
C3×#45332
C3×#19023
#703493