Finite Group Databasebeta

← C3×#70181 #11795378

Subgroups — C3×#70181 #11795378

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 460 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×#4977C211yesmaximal, characteristic, complemented
6C2×C3×#808C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2092—31nomaximal
9#70181C311yesmaximal, 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×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C32×#102—22no—
19C3×#832—22no—
20C3×C3⋊#95—22no—
21C3×#818—22no—
22C3×#808—22no—
23C2×C3×#107—31no—
24C2×C3×#106—31no—
25C2×C3×#102—21no—
26C2×C3×#102—31no—
27C2×C3×#102D311yescharacteristic
28C2×C3×#102C2×C311yescharacteristic
29C3×#390—31no—
30C3×#382—31no—
31#5221C2×C311yescharacteristic
32C2×#832C2×C311yescharacteristic
33C2×#818C2×C311yescharacteristic, complemented
34#4977C2×C311yescharacteristic, complemented
35C2×#808C2×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×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—21no—
67C22×C3×D4C2×D311yescharacteristic
68C22×C3×D4C22×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—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C22×C311yescharacteristic
78C2×C3×C22⋊C4—62no—
79C2×C3×C42—31no—
80C2×#217—22no—
81C2×C4⋊Dic3C22×C311yescharacteristic
82C2×C4⋊Dic3C22×C311yescharacteristic
83C2×C4×Dic3C22×C311yescharacteristic
84C22×C3⋊C8C22×C311yescharacteristic
85C3×#107—62no—
86C3×#106—62no—
87C3×#102—24no—
88C3×#102—22no—
89C3×#102—22no—
90C3×#102—62no—
91C3×#95—62no—
92#832—22no—
93C3⋊#95—22no—
94#818—22no—
95#808—22no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—42no—
100C23×C32—42no—
101C23×C32C2×D411yescharacteristic
102C32×D4—22no—
103C32×D4—22no—
104C32×D4—41no—
105C32×D4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—42no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×Q811yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C32×C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—31no—
124C2×#106—31no—
125C2×#102—31no—
126C2×#102C3×D311yescharacteristic
127#390—31no—
128#382—31no—
129#336—31no—
130C24×C3—21no—
131C24×C3—21no—
132C24×C3—41no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—21no—
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—22no—
146C2×C3×D4—41no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4Dic612yes—
150C2×C3×D4C3×Q812yes—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—32no—
155C22×C3×C4—41no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3C3×D412yes—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8#6712yes—
174C2×C3×C8C3×D412yes—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—124no—
186C3×C42—61no—
187C3×C42—61no—
188#217—44no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C4×Dic3—21no—
194C4×Dic3—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8C3×D412yes—
198C22×C32—42no—
199C22×C32—44no—
200C22×C32—82no—
201C22×C32—81no—
202C22×C32—81no—
203C22×C32C22⋊Q811yescharacteristic
204C22×C32#12311yescharacteristic
205C22×C32#12711yescharacteristic
206C22×C32#13512yes—
207C22×C32AGL(1,ℤ/8)12yes—
208C32×C4—81no—
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C32×C4#12311yescharacteristic
212C32×C4#12311yescharacteristic
213C3×Dic3—42no—
214C3×Dic3—81no—
215C3×Dic3—81no—
216C22×D4C2×C3×D311yescharacteristic
217C22×C8—31no—
218C22×C8C2×C3×D311yescharacteristic
219C2×C4⋊C4—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4C2×C3×D311yescharacteristic
222C2×C22⋊C4—62no—
223C2×C42—31no—
224#107—62no—
225#106—62no—
226#102—22no—
227#102—62no—
228#95—62no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—42no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—41no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—41no—
239C23×C3—41no—
240C23×C3—41no—
241C23×C3—42no—
242C23×C3—42no—
243C23×C3—82no—
244C23×C3—82no—
245C23×C3D3×D411yescharacteristic
246C23×C3C2×C3×D411yescharacteristic
247C3×D4—24no—
248C3×D4—22no—
249C3×D4—22no—
250C3×D4—22no—
251C3×D4—22no—
252C3×D4—42no—
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—42no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—82no—
274C2×C3×C4—122no—
275C2×C3×C4—122no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4C2×Dic611yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4#23711yescharacteristic
282C2×C3×C4#23711yescharacteristic
283C2×C3×C4C2×#6711yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×Q811yescharacteristic
287C2×C3×C4C3×#4111yescharacteristic
288C2×C3×C4C3×#4111yescharacteristic
289C2×C3×C4C3×#4111yescharacteristic
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—42no—
296C2×Dic3—42no—
297C3×C8—22no—
298C3×C8—22no—
299C3×C8—42no—
300C3×C8—62no—
301C3⋊C8—22no—
302C2×C32—82no—
303C2×C32#39911yescharacteristic
304C2×C32#47812yes—
305C2×C32#48212yes—
306C2×C32#49511yescharacteristic
307C2×C32#49611yescharacteristic
308C24—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4C3×Dic612yes—
315C22×C4—21no—
316C22×C4—32no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4C22×C3×D311yescharacteristic
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—32no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8C3×#6712yes—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C22⋊C4—124no—
333C42—61no—
334C42—61no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—44no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—44no—
344C22×C3—44no—
345C22×C3—84no—
346C22×C3—82no—
347C22×C3—84no—
348C22×C3—82no—
349C22×C3—81no—
350C22×C3—81no—
351C22×C3—82no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—81no—
355C22×C3#87811yescharacteristic
356C22×C3#88311yescharacteristic
357C22×C3#91212yes—
358C22×C3#91412yes—
359C22×C3#94011yescharacteristic
360C22×C3C3×C22⋊Q811yescharacteristic
361C22×C3C3×#12311yescharacteristic
362C22×C3C3×#12711yescharacteristic
363C22×C3C3×#13512yes—
364C22×C3C3×AGL(1,ℤ/8)12yes—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—82no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—122no—
373C3×C4—241no—
374C3×C4—241no—
375C3×C4#87811yescharacteristic
376C3×C4#88311yescharacteristic
377C3×C4#92411yescharacteristic
378C3×C4#93511yescharacteristic
379C3×C4C3×C22⋊Q811yescharacteristic
380C3×C4C3×C22⋊Q811yescharacteristic
381C3×C4C3×#12311yescharacteristic
382C3×C4C3×#12311yescharacteristic
383Dic3—42no—
384Dic3—81no—
385Dic3—81no—
386C32#209211yescharacteristic, complemented, Sylow
387C23—22no—
388C23—41no—
389C23—42no—
390C23—42no—
391C23—41no—
392C23C3×D3×D411yescharacteristic
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—122no—
403C2×C4—122no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4C2×C3×Dic611yescharacteristic
407C2×C4C3×#23511yescharacteristic
408C2×C4C3×D3×D411yescharacteristic
409C2×C4C3×#23711yescharacteristic
410C2×C4C3×#23711yescharacteristic
411C2×C4C2×C3×#6711yescharacteristic
412C8—22no—
413C8—62no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—21no—
419C2×C3—84no—
420C2×C3—82no—
421C2×C3—82no—
422C2×C3#476612yes—
423C2×C3#478412yes—
424C2×C3#494911yescharacteristic
425C2×C3#515511yescharacteristic
426C2×C3#517611yescharacteristic
427C2×C3C3×#39911yescharacteristic
428C2×C3C3×#47812yes—
429C2×C3C3×#48212yes—
430C2×C3C3×#49511yescharacteristic
431C2×C3C3×#49611yescharacteristic
432C22—42no—
433C22—44no—
434C22—81no—
435C22—82no—
436C22—81no—
437C22C3×#87811yescharacteristic
438C22C3×#88311yescharacteristic
439C22C3×#91212yes—
440C22C3×#91412yes—
441C22C3×#94011yescharacteristic
442C4—81no—
443C4—122no—
444C4—241no—
445C4—241no—
446C4C3×#87811yescharacteristic
447C4C3×#88311yescharacteristic
448C4C3×#92411yescharacteristic
449C4C3×#93511yescharacteristic
450C3—21no—
451C3#7018111yescharacteristic, direct product factor
452C3C3×#209211yescharacteristic, complemented
453C2—82no—
454C2C3×#476612yes—
455C2C3×#478412yes—
456C2C3×#494911yescharacteristic
457C2C3×#515511yescharacteristic
458C2C3×#517611yescharacteristic
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×#2092
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×#4977C2semidirect
6. C2×C3×#808C2semidirect
7. C3×#4550C2semidirect
9. #70181C3direct (N × H)
33. C2×#818C2×C3semidirect
34. #4977C2×C3semidirect
35. C2×#808C2×C3semidirect
37. #4550C2×C3semidirect
386. C32#2092semidirect
451. C3#70181direct (N × H)
452. C3C3×#2092semidirect

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×#49772
C2×C3×#8082
C3×#45502
C3×#20923
#701813