Finite Group Databasebeta

← C3×#70183 #11795424

Subgroups — C3×#70183 #11795424

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#102C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C3×#4975C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2093—31nomaximal
9#70183C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C3×#217—22no—
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×Dic3⋊C4—22no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C32×#102—22no—
20C3×#832—22no—
21C3×#818—22no—
22C3×#807—22no—
23C2×C3×#107—31no—
24C2×C3×#107—31no—
25C2×C3×#102—21no—
26C2×C3×#102—31no—
27C2×C3×#102D311yescharacteristic
28C2×C3×#102C2×C311yescharacteristic
29C3×#390—31no—
30C3×#384—31no—
31#5221C2×C311yescharacteristic
32C2×#832C2×C311yescharacteristic
33C2×#818C2×C311yescharacteristic, complemented
34#4975C2×C311yescharacteristic, complemented
35C2×#807C2×C311yescharacteristic, complemented
36C3×#336—31no—
37#4550C2×C311yescharacteristic, complemented
38C24×C32—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4Q812yes—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C3×#217—44no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
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—21no—
68C22×C3×D4C2×D311yescharacteristic
69C22×C3×D4C22×C311yescharacteristic
70C22×C3×C8—21no—
71C22×C3×C8—31no—
72C22×C3×C8C2×D311yescharacteristic
73C22×C3×C8C22×C311yescharacteristic
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—62no—
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C4⋊C4C22×C311yescharacteristic
80C2×C3×C22⋊C4—62no—
81C2×C3×C42—31no—
82C2×#217—22no—
83C2×C4⋊Dic3C22×C311yescharacteristic
84C2×C4⋊Dic3C22×C311yescharacteristic
85C2×Dic3⋊C4—22no—
86C2×C4×Dic3C22×C311yescharacteristic
87C22×C3⋊C8C22×C311yescharacteristic
88C3×#107—62no—
89C3×#107—62no—
90C3×#102—24no—
91C3×#102—22no—
92C3×#102—22no—
93C3×#102—62no—
94#832—22no—
95#818—22no—
96#807—22no—
97C23×C32—22no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—42no—
101C23×C32—42no—
102C23×C32C2×D411yescharacteristic
103C32×D4—22no—
104C32×D4—22no—
105C32×D4—41no—
106C32×D4—41no—
107C2×C32×C4—41no—
108C2×C32×C4—42no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×Q811yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3D814yes—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C2×#107—31no—
125C2×#107—31no—
126C2×#102—31no—
127C2×#102C3×D311yescharacteristic
128#390—31no—
129#384—31no—
130#336—31no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3—41no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—22no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C2×C3×D4Dic612yes—
151C2×C3×D4C3×Q812yes—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—41no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C23×C311yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3C3×D412yes—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—22no—
169C2×C3×C8—32no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8#6712yes—
175C2×C3×C8C3×D412yes—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—124no—
187C3×C22⋊C4—124no—
188C3×C42—61no—
189C3×C42—61no—
190#217—44no—
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195Dic3⋊C4—44no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8C3×D412yes—
201C22×C32—42no—
202C22×C32—44no—
203C22×C32—82no—
204C22×C32—81no—
205C22×C32—81no—
206C22×C32C22⋊Q811yescharacteristic
207C22×C32#12311yescharacteristic
208C22×C32#12711yescharacteristic
209C22×C32C2×D812yes—
210C22×C32#13712yes—
211C32×C4—81no—
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4#12311yescharacteristic
215C32×C4#12311yescharacteristic
216C3×Dic3—24no—
217C3×Dic3—81no—
218C3×Dic3—81no—
219C22×D4C2×C3×D311yescharacteristic
220C22×C8—31no—
221C22×C8C2×C3×D311yescharacteristic
222C2×C4⋊C4—31no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4C2×C3×D311yescharacteristic
226C2×C22⋊C4—62no—
227C2×C42—31no—
228#107—62no—
229#107—62no—
230#102—22no—
231#102—62no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—41no—
239C23×C3—42no—
240C23×C3—42no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—82no—
247C23×C3—82no—
248C23×C3D3×D411yescharacteristic
249C23×C3C2×C3×D411yescharacteristic
250C3×D4—24no—
251C3×D4—22no—
252C3×D4—22no—
253C3×D4—22no—
254C3×D4—22no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—42no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
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—34no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—82no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4C2×Dic611yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C2×C3×D411yescharacteristic
288C2×C3×C4C2×C3×D411yescharacteristic
289C2×C3×C4C2×C3×Q811yescharacteristic
290C2×C3×C4C3×#4111yescharacteristic
291C2×C3×C4C3×#4111yescharacteristic
292C2×C3×C4C3×#4111yescharacteristic
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—42no—
298C2×Dic3—42no—
299C2×Dic3C3×D814yes—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—42no—
303C3×C8—62no—
304C3⋊C8—22no—
305C2×C32—82no—
306C2×C32#39911yescharacteristic
307C2×C32#47412yes—
308C2×C32#48012yes—
309C2×C32#49311yescharacteristic
310C2×C32#49711yescharacteristic
311C24—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4C3×Dic612yes—
318C22×C4—21no—
319C22×C4—32no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4C22×C3×D311yescharacteristic
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—32no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8C3×#6712yes—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—124no—
336C22⋊C4—124no—
337C42—61no—
338C42—61no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—21no—
344C22×C3—44no—
345C22×C3—42no—
346C22×C3—44no—
347C22×C3—42no—
348C22×C3—44no—
349C22×C3—84no—
350C22×C3—82no—
351C22×C3—84no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3—82no—
356C22×C3—82no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3#87811yescharacteristic
360C22×C3#88311yescharacteristic
361C22×C3D3×D812yes—
362C22×C3#91512yes—
363C22×C3#94011yescharacteristic
364C22×C3C3×C22⋊Q811yescharacteristic
365C22×C3C3×#12311yescharacteristic
366C22×C3C3×#12711yescharacteristic
367C22×C3C2×C3×D812yes—
368C22×C3C3×#13712yes—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—64no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—241no—
378C3×C4—241no—
379C3×C4#87811yescharacteristic
380C3×C4#88311yescharacteristic
381C3×C4#92411yescharacteristic
382C3×C4#93511yescharacteristic
383C3×C4C3×C22⋊Q811yescharacteristic
384C3×C4C3×C22⋊Q811yescharacteristic
385C3×C4C3×#12311yescharacteristic
386C3×C4C3×#12311yescharacteristic
387Dic3—24no—
388Dic3—81no—
389Dic3—81no—
390C32#209311yescharacteristic, complemented, Sylow
391C23—22no—
392C23—41no—
393C23—42no—
394C23—42no—
395C23—41no—
396C23C3×D3×D411yescharacteristic
397D4—22no—
398D4—22no—
399D4—41no—
400D4—41no—
401C2×C4—34no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4C2×C3×Dic611yescharacteristic
411C2×C4C3×#23511yescharacteristic
412C2×C4C3×D3×D411yescharacteristic
413C2×C4C3×#23711yescharacteristic
414C2×C4C3×#23711yescharacteristic
415C2×C4C2×C3×#6711yescharacteristic
416C8—22no—
417C8—62no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—84no—
424C2×C3—82no—
425C2×C3—82no—
426C2×C3#475912yes—
427C2×C3#477412yes—
428C2×C3#494911yescharacteristic
429C2×C3#515111yescharacteristic
430C2×C3#516711yescharacteristic
431C2×C3C3×#39911yescharacteristic
432C2×C3C3×#47412yes—
433C2×C3C3×#48012yes—
434C2×C3C3×#49311yescharacteristic
435C2×C3C3×#49711yescharacteristic
436C22—42no—
437C22—44no—
438C22—81no—
439C22—82no—
440C22—81no—
441C22C3×#87811yescharacteristic
442C22C3×#88311yescharacteristic
443C22C3×D3×D812yes—
444C22C3×#91512yes—
445C22C3×#94011yescharacteristic
446C4—64no—
447C4—81no—
448C4—241no—
449C4—241no—
450C4C3×#87811yescharacteristic
451C4C3×#88311yescharacteristic
452C4C3×#92411yescharacteristic
453C4C3×#93511yescharacteristic
454C3—21no—
455C3#7018311yescharacteristic, direct product factor
456C3C3×#209311yescharacteristic, complemented
457C2—82no—
458C2C3×#475912yes—
459C2C3×#477412yes—
460C2C3×#494911yescharacteristic
461C2C3×#515111yescharacteristic
462C2C3×#516711yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC2×C3×#102D3
hypocenterC3C3×#2093
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C2×C3×#818C2semidirect
5. C3×#4975C2semidirect
6. C2×C3×#807C2semidirect
7. C3×#4550C2semidirect
9. #70183C3direct (N × H)
33. C2×#818C2×C3semidirect
34. #4975C2×C3semidirect
35. C2×#807C2×C3semidirect
37. #4550C2×C3semidirect
390. C32#2093semidirect
455. C3#70183direct (N × H)
456. C3C3×#2093semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1022
C3×#52212
C2×C3×#8322
C2×C3×#8182
C3×#49752
C2×C3×#8072
C3×#45502
C3×#20933
#701833