Finite Group Databasebeta

← C3×#70401 #11789710

Subgroups — C3×#70401 #11789710

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#421C211yesmaximal, characteristic
2C3×#5237C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C3×#5124C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6C3×#4533C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1932—31nomaximal
9#70401C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#104—22no—
18C3×#837—21no—
19C3×#837—21no—
20C3×#836C412yescomplemented
21C3×#833C412yescomplemented
22C3×#822—22no—
23C3×#815—21no—
24C3×C8×Dic3—21no—
25C3×#430—31no—
26C3×#421—21no—
27C3×#421D311yescharacteristic
28C3×#421C2×C311yescharacteristic
29C2×C3×#104—31no—
30C3×#413—31no—
31C3×C4×M16—31no—
32#5237C2×C311yescharacteristic
33C2×#837C2×C311yescharacteristic
34#5124C2×C311yescharacteristic, complemented
35Dic3×M16C2×C311yescharacteristic, complemented
36C3×#344—31no—
37C3×#339—31no—
38#4533C2×C311yescharacteristic, complemented
39#4532C2×C311yescharacteristic, complemented
40C32×#41—21no—
41C32×#41—21no—
42C32×#41—21no—
43C32×#41—21no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4C2×C411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50C32×M16—21no—
51C32×M16D412yes—
52C2×C32×C8—21no—
53C32×C4⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42—21no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3D411yescharacteristic
58C3×C4×Dic3D411yescharacteristic
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208C2×C412yes—
64C3×#208C2×C412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—31noSylow
69C2×C3×#41—21no—
70C2×C3×#41C2×D311yescharacteristic
71C2×C3×#41C22×C311yescharacteristic
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C3×#117—21no—
79C3×#117C2×D311yescharacteristic
80C3×#117C22×C311yescharacteristic
81C2×C3×C42—31no—
82C2×C4×Dic3C22×C311yescharacteristic
83C2×#208C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C2×#208C22×C311yescharacteristic
86C3×#108—62no—
87C3×#104—24no—
88C3×#104—22no—
89C3×#104—22no—
90C3×#104—61no—
91C3×#104—61no—
92C3×#101—32no—
93C3×#100—32no—
94C3×#97—61no—
95C3×C4×C8—61no—
96#837—21no—
97#837—21no—
98#836C3×C412yescomplemented
99#833C3×C412yescomplemented
100#822—22no—
101#815—21no—
102C8×Dic3—21no—
103C23×C32—21no—
104C23×C32#4111yescharacteristic
105C32×Q8—21no—
106C32×Q8—21no—
107C32×D4—21no—
108C32×D4—21no—
109C32×D4—41no—
110C32×D4—41no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—42no—
124C32×C8—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128#430—31no—
129#421C3×D311yescharacteristic
130C2×#104—31no—
131#413—31no—
132C4×M16—31no—
133#344—31no—
134#339—31no—
135C3×#41—22no—
136C3×#41—22no—
137C3×#41—21no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—21no—
145C3×#41—41no—
146C3×#41—41no—
147C2×C3×Q8—21no—
148C2×C3×Q8C4×D311yescharacteristic
149C2×C3×Q8C2×C3×C411yescharacteristic
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—41no—
154C2×C3×D4C4×D311yescharacteristic
155C2×C3×D4C2×C3×C411yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C23×C311yescharacteristic
163C22×Dic3—21no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—22no—
167C3×M16—32no—
168C3×M16—32no—
169C3×M16—41no—
170C3×M16—61no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16—61no—
174C3×M16#6712yes—
175C3×M16C3×D412yes—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—41no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—41no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—41no—
188C3×C42—22no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—61no—
194C4×Dic3—21no—
195C4×Dic3C3×D411yescharacteristic
196C4×Dic3C3×D411yescharacteristic
197#208—21no—
198#208—21no—
199#208—21no—
200#208—21no—
201#208C2×C3×C412yes—
202#208C2×C3×C412yes—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32—81no—
209C22×C32#11711yescharacteristic
210C22×C32#12311yescharacteristic
211C22×C32#12411yescharacteristic
212C32×C4—41no—
213C32×C4—81no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4#12611yescharacteristic
218C3×Dic3—22no—
219C3×Dic3—41no—
220C2×#41C2×C3×D311yescharacteristic
221C2×M16—31no—
222C2×M16—31no—
223C2×M16—31no—
224C2×M16C2×C3×D311yescharacteristic
225#117C2×C3×D311yescharacteristic
226C2×C42—31no—
227#108—62no—
228#104—22no—
229#104—61no—
230#104—61no—
231#101—32no—
232#100—32no—
233#97—61no—
234C4×C8—61no—
235C23×C3—21no—
236C23×C3—21no—
237C23×C3—21no—
238C23×C3—41no—
239C23×C3#23711yescharacteristic
240C23×C3C3×#4111yescharacteristic
241C3×Q8—22no—
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—21no—
245C3×Q8—21no—
246C3×Q8—41no—
247C3×D4—22no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—21no—
252C3×D4—41no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—41no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—42no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—122no—
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4#23711yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C22×C3×C411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C2×C3×C4C3×#4111yescharacteristic
290C2×C3×C4C3×#4111yescharacteristic
291C2×C3×C4C3×#4111yescharacteristic
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—42no—
295C3×C8—22no—
296C3×C8—22no—
297C3×C8—42no—
298C3×C8—62no—
299C3×C8—62no—
300C3×C8—121no—
301C3⋊C8—22no—
302C3⋊C8—22no—
303C3⋊C8—41no—
304C2×C32—21no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—81no—
308C2×C32#38811yescharacteristic
309#41—21no—
310#41—21no—
311#41—21no—
312#41—21no—
313C2×Q8C3×C4×D311yescharacteristic
314C2×D4—21no—
315C2×D4C3×C4×D311yescharacteristic
316C22×C4—21no—
317C22×C4—61no—
318C22×C4C22×C3×D311yescharacteristic
319M16—21no—
320M16—32no—
321M16—32no—
322M16—61no—
323M16—61no—
324M16—61no—
325M16—61no—
326M16C3×#6712yes—
327C2×C8—21no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C4⋊C4—21no—
332C22⋊C4—21no—
333C42—21no—
334C42—31no—
335C42—31no—
336C42—61no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—42no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—81no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—82no—
349C22×C3#87711yescharacteristic
350C22×C3#88311yescharacteristic
351C22×C3#93611yescharacteristic
352C22×C3C3×#11711yescharacteristic
353C22×C3C3×#12311yescharacteristic
354C22×C3C3×#12411yescharacteristic
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—42no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—62no—
363C3×C4—81no—
364C3×C4—81no—
365C3×C4—82no—
366C3×C4—121no—
367C3×C4#87911yescharacteristic
368C3×C4#67⋊C411yescharacteristic
369C3×C4C4×#6711yescharacteristic
370C3×C4#93911yescharacteristic
371C3×C4C3×C4×D411yescharacteristic
372C3×C4C3×C4×D411yescharacteristic
373C3×C4C3×#12111yescharacteristic
374C3×C4C3×#12611yescharacteristic
375Dic3—22no—
376Dic3—41no—
377C32#193211yescharacteristic, complemented, Sylow
378C23—21no—
379C23C3×#23711yescharacteristic
380Q8—21no—
381Q8—21no—
382D4—21no—
383D4—21no—
384D4—41no—
385D4—41no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—122no—
393C2×C4C2×C3×C4×D311yescharacteristic
394C2×C4C3×#23511yescharacteristic
395C2×C4C3×D3×D411yescharacteristic
396C2×C4C3×#23711yescharacteristic
397C2×C4C3×#23711yescharacteristic
398C2×C4C2×C3×#6711yescharacteristic
399C8—22no—
400C8—62no—
401C8—62no—
402C8—121no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3—82no—
414C2×C3—81no—
415C2×C3—81no—
416C2×C3#494511yescharacteristic
417C2×C3C3×#38811yescharacteristic
418C22—41no—
419C22—41no—
420C22—81no—
421C22C3×#87711yescharacteristic
422C22C3×#88311yescharacteristic
423C22C3×#93611yescharacteristic
424C4—41no—
425C4—62no—
426C4—81no—
427C4—121no—
428C4C3×#87911yescharacteristic
429C4C3×#67⋊C411yescharacteristic
430C4C3×C4×#6711yescharacteristic
431C4C3×#93911yescharacteristic
432C3—21no—
433C3#7040111yescharacteristic, direct product factor
434C3C3×#193211yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—81no—
439C2C3×#494511yescharacteristic
subgroupG/H
centerC3×C4#939
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#421C2
socleC2×C32#388
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#421D3
hypocenterC3C3×#1932
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
4. C3×#5124C2semidirect
5. C3×Dic3×M16C2semidirect
6. C3×#4533C2semidirect
7. C3×#4532C2semidirect
9. #70401C3direct (N × H)
20. C3×#836C4semidirect
21. C3×#833C4semidirect
34. #5124C2×C3semidirect
35. Dic3×M16C2×C3semidirect
38. #4533C2×C3semidirect
39. #4532C2×C3semidirect
98. #836C3×C4semidirect
99. #833C3×C4semidirect
377. C32#1932semidirect
433. C3#70401direct (N × H)
434. C3C3×#1932semidirect

Maximal subgroups

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

subgroupindex
C32×#4212
C3×#52372
C2×C3×#8372
C3×#51242
C3×Dic3×M162
C3×#45332
C3×#45322
C3×#19323
#704013