Finite Group Databasebeta

← C3×#70640 #11795375

Subgroups — C3×#70640 #11795375

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#107C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3C3×#4988C211yesmaximal, characteristic
4C3×#4977C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C2×C3×#808C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2092—31nomaximal
9#70640C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C32×#107—22no—
19C3×C3⋊#95—22no—
20C3×#821—22no—
21C3×#809—22no—
22C3×#808—22no—
23C2×C3×#107—21no—
24C2×C3×#107D311yescharacteristic, complemented
25C2×C3×#107C2×C311yescharacteristic, complemented
26C2×C3×#106—31no—
27C2×C3×#102—31no—
28C2×C3×#102—31no—
29C3×#390—31no—
30C3×#382—31no—
31C2×#821C2×C311yescharacteristic
32#4988C2×C311yescharacteristic
33#4977C2×C311yescharacteristic, complemented
34C2×#809C2×C311yescharacteristic
35C2×#808C2×C311yescharacteristic, complemented
36C3×#336—31no—
37#4550C2×C311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3×Dic3—21no—
43C22×C3×Dic3D412yes—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C3×(C2×D3)⋊C4—44no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#2092—31noSylow
66C22×C3×D4—31no—
67C22×D12C22×C311yescharacteristic
68C22×C3×C8—21no—
69C22×C3×C8—31no—
70C22×C3×C8C2×D311yescharacteristic
71C22×C3×C8C22×C311yescharacteristic
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C22×C311yescharacteristic
78C2×C3×C4⋊C4C22×C311yescharacteristic
79C2×C3×C22⋊C4—62no—
80C2×C3×C42—31no—
81C2×(C2×D3)⋊C4—22no—
82C2×C4⋊Dic3C22×C311yescharacteristic
83C2×C4×Dic3C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#107—24no—
86C3×#107—22no—
87C3×#107—22no—
88C3×#106—62no—
89C3×#102—62no—
90C3×#102—62no—
91C3×#95—62no—
92C3⋊#95—22no—
93#821—22no—
94#809—22no—
95#808—22no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—42no—
105C2×C32×C4—42no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×Q811yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C32×C8—22no—
122C3×C3⋊C8—22no—
123C2×#107C3×D311yescharacteristic, complemented
124C2×#106—31no—
125C2×#102—31no—
126C2×#102—31no—
127#390—31no—
128#382—31no—
129#336—31no—
130C24×C3—61no—
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—32no—
144C22×C3×C4—41no—
145C22×C3×C4—41no—
146C22×C3×C4—61no—
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C23×C311yescharacteristic
149C22×Dic3—21no—
150C22×Dic3C3×D412yes—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12C3×Q812yes—
157C2×C3×C8—22no—
158C2×C3×C8—22no—
159C2×C3×C8—21no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—22no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8#6712yes—
168C2×C3×C8C3×D412yes—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—124no—
184C3×C42—61no—
185C3×C42—61no—
186(C2×D3)⋊C4—44no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4×Dic3—21no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8C3×D412yes—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32#12311yescharacteristic
196C22×C32#12711yescharacteristic
197C22×C32#13512yes—
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3×D3—42no—
200C2×C3×D3—44no—
201C2×C3×D3—82no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C32×C4—81no—
205C32×C4—81no—
206C32×C4C22⋊Q811yescharacteristic
207C32×C4C22⋊Q811yescharacteristic
208C32×C4#12311yescharacteristic
209C32×C4#12311yescharacteristic
210C3×Dic3—42no—
211C3×Dic3—81no—
212C22×D4—31no—
213C22×C8—31no—
214C22×C8C2×C3×D311yescharacteristic
215C2×C4⋊C4—31no—
216C2×C4⋊C4C2×C3×D311yescharacteristic
217C2×C4⋊C4C2×C3×D311yescharacteristic
218C2×C22⋊C4—62no—
219C2×C42—31no—
220#107—22no—
221#106—62no—
222#102—62no—
223#102—62no—
224#95—62no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—121no—
228C23×C3—122no—
229C23×C3—122no—
230C23×C3—121no—
231C23×C3D3×D411yescharacteristic
232C23×C3C2×C3×D411yescharacteristic
233C22×D3—22no—
234C22×D3—41no—
235C22×D3—41no—
236C22×D3—42no—
237C22×D3—42no—
238C3×D4—62no—
239C3×D4—62no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—82no—
262C2×C3×C4—82no—
263C2×C3×C4—122no—
264C2×C3×C4—121no—
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4#23911yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×C3×D411yescharacteristic
272C2×C3×C4C2×C3×D411yescharacteristic
273C2×C3×C4C2×C3×Q811yescharacteristic
274C2×C3×C4C3×#4111yescharacteristic
275C2×C3×C4C3×#4111yescharacteristic
276C2×C3×C4C3×#4111yescharacteristic
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—41no—
281C2×Dic3—42no—
282D12—22no—
283D12—22no—
284D12—41no—
285D12—41no—
286C3×C8—24no—
287C3×C8—22no—
288C3×C8—22no—
289C3×C8—62no—
290C3⋊C8—22no—
291C2×C32#39911yescharacteristic
292C2×C32#47812yes—
293C2×C32#48212yes—
294C2×C32#49511yescharacteristic
295C2×C32#49611yescharacteristic
296C3×D3—82no—
297C24—61no—
298C2×D4—32no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—32no—
307C22×C4—61no—
308C22×C4C22×C3×D311yescharacteristic
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—32no—
312C2×C8—61no—
313C2×C8—61no—
314C2×C8C3×#6712yes—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—61no—
320C4⋊C4—61no—
321C22⋊C4—124no—
322C42—61no—
323C42—61no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—124no—
330C22×C3—122no—
331C22×C3—242no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3#89411yescharacteristic
335C22×C3#89611yescharacteristic
336C22×C3#91112yes—
337C22×C3#91912yes—
338C22×C3#94011yescharacteristic
339C22×C3C3×C22⋊Q811yescharacteristic
340C22×C3C3×#12311yescharacteristic
341C22×C3C3×#12711yescharacteristic
342C22×C3C3×#13512yes—
343C22×C3C3×AGL(1,ℤ/8)12yes—
344C2×D3—42no—
345C2×D3—44no—
346C2×D3—82no—
347C2×D3—81no—
348C2×D3—81no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—82no—
354C3×C4—82no—
355C3×C4—81no—
356C3×C4—81no—
357C3×C4—81no—
358C3×C4—81no—
359C3×C4—122no—
360C3×C4—241no—
361C3×C4#89411yescharacteristic
362C3×C4#89611yescharacteristic
363C3×C4#92911yescharacteristic
364C3×C4#94611yescharacteristic
365C3×C4C3×C22⋊Q811yescharacteristic
366C3×C4C3×C22⋊Q811yescharacteristic
367C3×C4C3×#12311yescharacteristic
368C3×C4C3×#12311yescharacteristic
369Dic3—42no—
370Dic3—81no—
371C32#209211yescharacteristic, complemented, Sylow
372C23—62no—
373C23—121no—
374C23—122no—
375C23—122no—
376C23—121no—
377C23C3×D3×D411yescharacteristic
378D4—62no—
379D4—62no—
380D4—121no—
381D4—121no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—62no—
389C2×C4—122no—
390C2×C4—121no—
391C2×C4C3×#23511yescharacteristic
392C2×C4C3×#23511yescharacteristic
393C2×C4C3×D3×D411yescharacteristic
394C2×C4C3×D3×Q811yescharacteristic
395C2×C4C3×#23911yescharacteristic
396C2×C4C2×C3×#6711yescharacteristic
397C8—22no—
398C8—62no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—22no—
402C2×C3—22no—
403C2×C3—21no—
404C2×C3—242no—
405C2×C3#488512yes—
406C2×C3#489112yes—
407C2×C3#499311yescharacteristic
408C2×C3#515411yescharacteristic
409C2×C3#519111yescharacteristic
410C2×C3C3×#39911yescharacteristic
411C2×C3C3×#47812yes—
412C2×C3C3×#48212yes—
413C2×C3C3×#49511yescharacteristic
414C2×C3C3×#49611yescharacteristic
415D3—82no—
416C22—122no—
417C22—124no—
418C22—241no—
419C22—242no—
420C22—241no—
421C22C3×#89411yescharacteristic
422C22C3×#89611yescharacteristic
423C22C3×#91112yes—
424C22C3×#91912yes—
425C22C3×#94011yescharacteristic
426C4—81no—
427C4—81no—
428C4—122no—
429C4—241no—
430C4C3×#89411yescharacteristic
431C4C3×#89611yescharacteristic
432C4C3×#92911yescharacteristic
433C4C3×#94611yescharacteristic
434C3—21no—
435C3#7064011yescharacteristic, direct product factor
436C3C3×#209211yescharacteristic, complemented
437C2—242no—
438C2C3×#488512yes—
439C2C3×#489112yes—
440C2C3×#499311yescharacteristic
441C2C3×#515411yescharacteristic
442C2C3×#519111yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#107C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×#107D3
hypocenterC3C3×#2092
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#107

Complements

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

NH ≅ G/Ntype
1. C2×C32×#107C2semidirect
4. C3×#4977C2semidirect
6. C2×C3×#808C2semidirect
7. C3×#4550C2semidirect
9. #70640C3direct (N × H)
24. C2×C3×#107D3semidirect
25. C2×C3×#107C2×C3semidirect
33. #4977C2×C3semidirect
35. C2×#808C2×C3semidirect
37. #4550C2×C3semidirect
123. C2×#107C3×D3semidirect
371. C32#2092semidirect
435. C3#70640direct (N × H)
436. C3C3×#2092semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1072
C2×C3×#8212
C3×#49882
C3×#49772
C2×C3×#8092
C2×C3×#8082
C3×#45502
C3×#20923
#706403