Finite Group Databasebeta

← C3×#70130 #11789707

Subgroups — C3×#70130 #11789707

Order 1152.

507 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×#413C211yesmaximal, characteristic
2C3×#5236C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C3×#5125C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8C3×#1932—31nomaximal
9#70130C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#101C412yescomplemented
18C32×#100C412yescomplemented
19C3×#837—21no—
20C3×#837—21no—
21C3×#837—22no—
22C3×#819—22no—
23C3×#815—21no—
24C3×C8×Dic3—21no—
25C3×#430—31no—
26C3×#421—31no—
27C2×C3×#104—31no—
28C3×#413—21no—
29C3×#413D311yescharacteristic
30C3×#413C2×C311yescharacteristic
31C3×C4×M16—31no—
32#5236C2×C311yescharacteristic
33C2×#837C2×C311yescharacteristic
34#5125C2×C311yescharacteristic, complemented
35Dic3×M16C2×C311yescharacteristic, complemented
36C3×#344—31no—
37C3×#339—31no—
38#4559C2×C311yescharacteristic, complemented
39#4555C2×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×M16—21no—
52C32×M16C2×C412yes—
53C32×M16C2×C412yes—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208D412yes—
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—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C22×C311yescharacteristic
79C2×C3×M16C22×C311yescharacteristic
80C3×#117—31no—
81C2×C3×C42—31no—
82#926C22×C311yescharacteristic
83C2×C4×Dic3C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C2×#208C22×C311yescharacteristic
86C3×#108—62no—
87C3×#104—61no—
88C3×#104—61no—
89C3×#104—62no—
90C3×#101—22no—
91C3×#101Dic312yescomplemented
92C3×#101C3×C412yescomplemented
93C3×#100—22no—
94C3×#100Dic312yescomplemented
95C3×#100C3×C412yescomplemented
96C3×#97—61no—
97C3×C4×C8—61no—
98#837—21no—
99#837—21no—
100#837—22no—
101#819—22no—
102#815—21no—
103C8×Dic3—21no—
104C23×C32—21no—
105C23×C32#4111yescharacteristic
106C32×Q8—21no—
107C32×Q8—21no—
108C32×D4—21no—
109C32×D4—21no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4—21no—
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—
124C2×C3×Dic3—41no—
125C32×C8—22no—
126C32×C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#430—31no—
130#421—31no—
131C2×#104—31no—
132#413C3×D311yescharacteristic
133C4×M16—31no—
134#344—31no—
135#339—31no—
136C3×#41—21no—
137C3×#41—21no—
138C3×#41—21no—
139C3×#41—21no—
140C3×#41—21no—
141C3×#41—21no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41—41no—
145C3×#41—41no—
146C3×#41—41no—
147C3×#41—41no—
148C2×C3×Q8—21no—
149C2×C3×Q8C2×Dic311yescharacteristic
150C2×C3×Q8C2×C3×C411yescharacteristic
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4C2×Dic311yescharacteristic
156C2×C3×D4C2×C3×C411yescharacteristic
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C22×Dic3—21no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—21no—
168C3×M16—21no—
169C3×M16—22no—
170C3×M16—22no—
171C3×M16—32no—
172C3×M16—41no—
173C3×M16—41no—
174C3×M16—61no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16C2×Dic312yes—
178C3×M16C2×Dic312yes—
179C3×M16C2×C3×C412yes—
180C3×M16C2×C3×C412yes—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—41no—
186C2×C3×C8—41no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—61no—
194C3×C42—61no—
195#217—21no—
196C4⋊Dic3—21no—
197C4×Dic3—21no—
198C4×Dic3—21no—
199C4×Dic3C3×D411yescharacteristic
200C4×Dic3C3×D411yescharacteristic
201#208—21no—
202#208—21no—
203#208—21no—
204#208C3×D412yes—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32—81no—
210C22×C32#11711yescharacteristic
211C22×C32#12311yescharacteristic
212C22×C32#12411yescharacteristic
213C32×C4—41no—
214C32×C4C4×D411yescharacteristic
215C32×C4C4×D411yescharacteristic
216C32×C4#12111yescharacteristic
217C32×C4#12611yescharacteristic
218C3×Dic3—22no—
219C3×Dic3—41no—
220C3×Dic3—81no—
221C2×#41C2×C3×D311yescharacteristic
222C2×M16—31no—
223C2×M16—31no—
224C2×M16C2×C3×D311yescharacteristic
225C2×M16C2×C3×D311yescharacteristic
226#117—31no—
227C2×C42—31no—
228#108—62no—
229#104—61no—
230#104—61no—
231#104—62no—
232#101C3×Dic312yescomplemented
233#100C3×Dic312yescomplemented
234#97—61no—
235C4×C8—61no—
236C23×C3—22no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3#23511yescharacteristic
241C23×C3C3×#4111yescharacteristic
242C3×Q8—21no—
243C3×Q8—21no—
244C3×Q8—21no—
245C3×Q8—21no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×D4—21no—
249C3×D4—21no—
250C3×D4—21no—
251C3×D4—21no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C2×C3×C4—22no—
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—21no—
268C2×C3×C4—21no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—122no—
278C2×C3×C4—121no—
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4#23711yescharacteristic
284C2×C3×C4C22×Dic311yescharacteristic
285C2×C3×C4C22×C3×C411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C3×#4111yescharacteristic
289C2×C3×C4C3×#4111yescharacteristic
290C2×C3×C4C3×#4111yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—42no—
294C2×Dic3—41no—
295C3×C8—22no—
296C3×C8—22no—
297C3×C8—22no—
298C3×C8—22no—
299C3×C8—42no—
300C3×C8—42no—
301C3×C8—62no—
302C3×C8—121no—
303C3⋊C8—22no—
304C3⋊C8—41no—
305C2×C32—21no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32—81no—
309C2×C32#38811yescharacteristic
310#41—21no—
311#41—21no—
312#41—21no—
313#41—21no—
314C2×Q8C2×C3×Dic311yescharacteristic
315C2×D4—21no—
316C2×D4C2×C3×Dic311yescharacteristic
317C22×C4—21no—
318C22×C4—61no—
319C22×C4C22×C3×D311yescharacteristic
320M16—21no—
321M16—21no—
322M16—32no—
323M16—61no—
324M16—61no—
325M16—61no—
326M16C2×C3×Dic312yes—
327M16C2×C3×Dic312yes—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—61no—
331C2×C8—61no—
332C4⋊C4—61no—
333C22⋊C4—61no—
334C42—31no—
335C42—31no—
336C42—61no—
337C42—61no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—81no—
347C22×C3—81no—
348C22×C3—81no—
349C22×C3—82no—
350C22×C3#88311yescharacteristic
351C22×C3#88511yescharacteristic
352C22×C3#92611yescharacteristic
353C22×C3C3×#11711yescharacteristic
354C22×C3C3×#12311yescharacteristic
355C22×C3C3×#12411yescharacteristic
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—42no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—62no—
364C3×C4—121no—
365C3×C4—241no—
366C3×C4#87911yescharacteristic
367C3×C4#88411yescharacteristic
368C3×C4D4×Dic311yescharacteristic
369C3×C4D4×Dic311yescharacteristic
370C3×C4C3×C4×D411yescharacteristic
371C3×C4C3×C4×D411yescharacteristic
372C3×C4C3×#12111yescharacteristic
373C3×C4C3×#12611yescharacteristic
374Dic3—22no—
375Dic3—41no—
376Dic3—81no—
377C32#193211yescharacteristic, complemented, Sylow
378C23—21no—
379C23C3×#23511yescharacteristic
380Q8—21no—
381Q8—21no—
382D4—21no—
383D4—21no—
384D4—41no—
385D4—41no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—122no—
392C2×C4—121no—
393C2×C4C3×#23511yescharacteristic
394C2×C4C3×D3×D411yescharacteristic
395C2×C4C3×D3×D411yescharacteristic
396C2×C4C3×#23711yescharacteristic
397C2×C4C3×#23711yescharacteristic
398C2×C4C22×C3×Dic311yescharacteristic
399C8—22no—
400C8—22no—
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#495111yescharacteristic
417C2×C3C3×#38811yescharacteristic
418C22—41no—
419C22—41no—
420C22—81no—
421C22C3×#88311yescharacteristic
422C22C3×#88511yescharacteristic
423C22C3×#92611yescharacteristic
424C4—41no—
425C4—62no—
426C4—121no—
427C4—241no—
428C4C3×#87911yescharacteristic
429C4C3×#88411yescharacteristic
430C4C3×D4×Dic311yescharacteristic
431C4C3×D4×Dic311yescharacteristic
432C3—21no—
433C3#7013011yescharacteristic, direct product factor
434C3C3×#193211yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—81no—
439C2C3×#495111yescharacteristic
subgroupG/H
centerC3×C4#884
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#413C2
socleC2×C32#388
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#413D3
hypocenterC3C3×#1932
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
4. C3×#5125C2semidirect
5. C3×Dic3×M16C2semidirect
6. C3×#4559C2semidirect
7. C3×#4555C2semidirect
9. #70130C3direct (N × H)
17. C32×#101C4semidirect
18. C32×#100C4semidirect
34. #5125C2×C3semidirect
35. Dic3×M16C2×C3semidirect
38. #4559C2×C3semidirect
39. #4555C2×C3semidirect
91. C3×#101Dic3semidirect
92. C3×#101C3×C4semidirect
94. C3×#100Dic3semidirect
95. C3×#100C3×C4semidirect
232. #101C3×Dic3semidirect
233. #100C3×Dic3semidirect
377. C32#1932semidirect
433. C3#70130direct (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×#4132
C3×#52362
C2×C3×#8372
C3×#51252
C3×Dic3×M162
C3×#45592
C3×#45552
C3×#19323
#701303