Finite Group Databasebeta

← C3×#70641 #11795421

Subgroups — C3×#70641 #11795421

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 448 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×#4975C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2093—31nomaximal
9#70641C311yesmaximal, 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×Dic3⋊C4—22no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C32×#107—22no—
20C3×#821—22no—
21C3×#809—22no—
22C3×#807—22no—
23C2×C3×#107—21no—
24C2×C3×#107—31no—
25C2×C3×#107D311yescharacteristic, complemented
26C2×C3×#107C2×C311yescharacteristic, complemented
27C2×C3×#102—31no—
28C2×C3×#102—31no—
29C3×#390—31no—
30C3×#384—31no—
31C2×#821C2×C311yescharacteristic
32#4988C2×C311yescharacteristic
33#4975C2×C311yescharacteristic, complemented
34C2×#809C2×C311yescharacteristic
35C2×#807C2×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×Dic3⋊C4—44no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8D412yes—
66#2093—31noSylow
67C22×C3×D4—31no—
68C22×D12C22×C311yescharacteristic
69C22×C3×C8—21no—
70C22×C3×C8—31no—
71C22×C3×C8C2×D311yescharacteristic
72C22×C3×C8C22×C311yescharacteristic
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—62no—
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C4⋊C4C22×C311yescharacteristic
80C2×C3×C4⋊C4C22×C311yescharacteristic
81C2×C3×C22⋊C4—62no—
82C2×C3×C42—31no—
83C2×(C2×D3)⋊C4—22no—
84C2×C4⋊Dic3C22×C311yescharacteristic
85C2×Dic3⋊C4—22no—
86C2×C4×Dic3C22×C311yescharacteristic
87C22×C3⋊C8C22×C311yescharacteristic
88C3×#107—24no—
89C3×#107—22no—
90C3×#107—22no—
91C3×#107—62no—
92C3×#102—62no—
93C3×#102—62no—
94#821—22no—
95#809—22no—
96#807—22no—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—22no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C22×C3×D3—42no—
102C22×C3×D3—42no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—42no—
106C2×C32×C4—42no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×Q811yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3D814yes—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C2×#107—31no—
125C2×#107C3×D311yescharacteristic, complemented
126C2×#102—31no—
127C2×#102—31no—
128#390—31no—
129#384—31no—
130#336—31no—
131C24×C3—61no—
132C23×D3—21no—
133C2×C3×D4—32no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—32no—
145C22×C3×C4—41no—
146C22×C3×C4—41no—
147C22×C3×C4—61no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C23×C311yescharacteristic
150C22×Dic3—21no—
151C22×Dic3C3×D412yes—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12C3×Q812yes—
158C2×C3×C8—22no—
159C2×C3×C8—22no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—22no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8#6712yes—
169C2×C3×C8C3×D412yes—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—22no—
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—21no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—124no—
185C3×C22⋊C4—124no—
186C3×C42—61no—
187C3×C42—61no—
188(C2×D3)⋊C4—44no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191Dic3⋊C4—44no—
192C4×Dic3—21no—
193C4×Dic3—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8C3×D412yes—
197C22×C32C22⋊Q811yescharacteristic
198C22×C32#12311yescharacteristic
199C22×C32#12711yescharacteristic
200C22×C32C2×D812yes—
201C22×C32#13712yes—
202C2×C3×D3—42no—
203C2×C3×D3—44no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C32×C4—81no—
208C32×C4—81no—
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C32×C4#12311yescharacteristic
212C32×C4#12311yescharacteristic
213C3×Dic3—24no—
214C3×Dic3—81no—
215C22×D4—31no—
216C22×C8—31no—
217C22×C8C2×C3×D311yescharacteristic
218C2×C4⋊C4—31no—
219C2×C4⋊C4—62no—
220C2×C4⋊C4C2×C3×D311yescharacteristic
221C2×C4⋊C4C2×C3×D311yescharacteristic
222C2×C22⋊C4—62no—
223C2×C42—31no—
224#107—22no—
225#107—62no—
226#102—62no—
227#102—62no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—121no—
231C23×C3—122no—
232C23×C3—122no—
233C23×C3—121no—
234C23×C3D3×D411yescharacteristic
235C23×C3C2×C3×D411yescharacteristic
236C22×D3—22no—
237C22×D3—41no—
238C22×D3—41no—
239C22×D3—42no—
240C22×D3—42no—
241C3×D4—62no—
242C3×D4—62no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—34no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—82no—
265C2×C3×C4—82no—
266C2×C3×C4—122no—
267C2×C3×C4—121no—
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×Q811yescharacteristic
272C2×C3×C4#23911yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×C3×C4C2×C3×D411yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×C3×C4C2×C3×Q811yescharacteristic
277C2×C3×C4C3×#4111yescharacteristic
278C2×C3×C4C3×#4111yescharacteristic
279C2×C3×C4C3×#4111yescharacteristic
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—41no—
283C2×Dic3—42no—
284C2×Dic3C3×D814yes—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—24no—
290C3×C8—22no—
291C3×C8—22no—
292C3×C8—62no—
293C3⋊C8—22no—
294C2×C32#39911yescharacteristic
295C2×C32#47412yes—
296C2×C32#48012yes—
297C2×C32#49311yescharacteristic
298C2×C32#49711yescharacteristic
299C3×D3—82no—
300C24—61no—
301C2×D4—32no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—32no—
310C22×C4—61no—
311C22×C4C22×C3×D311yescharacteristic
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—32no—
315C2×C8—61no—
316C2×C8—61no—
317C2×C8C3×#6712yes—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—124no—
325C22⋊C4—124no—
326C42—61no—
327C42—61no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—124no—
334C22×C3—122no—
335C22×C3—242no—
336C22×C3—241no—
337C22×C3—241no—
338C22×C3#89411yescharacteristic
339C22×C3#89611yescharacteristic
340C22×C3D3×D812yes—
341C22×C3#91812yes—
342C22×C3#94011yescharacteristic
343C22×C3C3×C22⋊Q811yescharacteristic
344C22×C3C3×#12311yescharacteristic
345C22×C3C3×#12711yescharacteristic
346C22×C3C2×C3×D812yes—
347C22×C3C3×#13712yes—
348C2×D3—42no—
349C2×D3—44no—
350C2×D3—82no—
351C2×D3—81no—
352C2×D3—81no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—64no—
358C3×C4—82no—
359C3×C4—82no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4—81no—
363C3×C4—81no—
364C3×C4—241no—
365C3×C4#89411yescharacteristic
366C3×C4#89611yescharacteristic
367C3×C4#92911yescharacteristic
368C3×C4#94611yescharacteristic
369C3×C4C3×C22⋊Q811yescharacteristic
370C3×C4C3×C22⋊Q811yescharacteristic
371C3×C4C3×#12311yescharacteristic
372C3×C4C3×#12311yescharacteristic
373Dic3—24no—
374Dic3—81no—
375C32#209311yescharacteristic, complemented, Sylow
376C23—62no—
377C23—121no—
378C23—122no—
379C23—122no—
380C23—121no—
381C23C3×D3×D411yescharacteristic
382D4—62no—
383D4—62no—
384D4—121no—
385D4—121no—
386C2×C4—34no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—122no—
394C2×C4—121no—
395C2×C4C3×#23511yescharacteristic
396C2×C4C3×#23511yescharacteristic
397C2×C4C3×D3×D411yescharacteristic
398C2×C4C3×D3×Q811yescharacteristic
399C2×C4C3×#23911yescharacteristic
400C2×C4C2×C3×#6711yescharacteristic
401C8—22no—
402C8—62no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—242no—
409C2×C3#488212yes—
410C2×C3#489012yes—
411C2×C3#499311yescharacteristic
412C2×C3#515111yescharacteristic
413C2×C3#519011yescharacteristic
414C2×C3C3×#39911yescharacteristic
415C2×C3C3×#47412yes—
416C2×C3C3×#48012yes—
417C2×C3C3×#49311yescharacteristic
418C2×C3C3×#49711yescharacteristic
419D3—82no—
420C22—122no—
421C22—124no—
422C22—241no—
423C22—242no—
424C22—241no—
425C22C3×#89411yescharacteristic
426C22C3×#89611yescharacteristic
427C22C3×D3×D812yes—
428C22C3×#91812yes—
429C22C3×#94011yescharacteristic
430C4—64no—
431C4—81no—
432C4—81no—
433C4—241no—
434C4C3×#89411yescharacteristic
435C4C3×#89611yescharacteristic
436C4C3×#92911yescharacteristic
437C4C3×#94611yescharacteristic
438C3—21no—
439C3#7064111yescharacteristic, direct product factor
440C3C3×#209311yescharacteristic, complemented
441C2—242no—
442C2C3×#488212yes—
443C2C3×#489012yes—
444C2C3×#499311yescharacteristic
445C2C3×#515111yescharacteristic
446C2C3×#519011yescharacteristic
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×#2093
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×#4975C2semidirect
6. C2×C3×#807C2semidirect
7. C3×#4550C2semidirect
9. #70641C3direct (N × H)
25. C2×C3×#107D3semidirect
26. C2×C3×#107C2×C3semidirect
33. #4975C2×C3semidirect
35. C2×#807C2×C3semidirect
37. #4550C2×C3semidirect
125. C2×#107C3×D3semidirect
375. C32#2093semidirect
439. C3#70641direct (N × H)
440. C3C3×#2093semidirect

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×#49752
C2×C3×#8092
C2×C3×#8072
C3×#45502
C3×#20933
#706413