Finite Group Databasebeta

← C3×#69001 #11785612

Subgroups — C3×#69001 #11785612

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#907C211yesmaximal, characteristic
2C3×#5133C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4C3×#4966C211yesmaximal, characteristic
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C32×#343C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#1816—31nomaximal
9#69001C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#907—22no—
18C3×#907C414yescomplemented
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C3×#822—22no—
22C3×#821—21no—
23C3×#816—21no—
24C3×#810—21no—
25C3×#809—21no—
26C3×#807—21no—
27C3×#807—21no—
28C2×C3×#131—31no—
29C2×#907C2×C311yescharacteristic
30C2×C3×#108—31no—
31C2×C3×#107—31no—
32C3×#417—31no—
33C3×#417—31no—
34#5133C2×C311yescharacteristic
35C2×#822C2×C311yescharacteristic, complemented
36#4966C2×C311yescharacteristic
37C2×#807C2×C311yescharacteristic, complemented
38C3×#343—21no—
39C3×#343—31no—
40C3×#343D311yescharacteristic, complemented
41C3×#343C2×C311yescharacteristic, complemented
42#4554C2×C311yescharacteristic, complemented
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235Q812yes—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×M16—21no—
55C32×M16—21no—
56C32×M16—21no—
57C32×M16C2×C412yes—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D411yescharacteristic
70C2×C3×C3⋊C8D412yes—
71C3×ΓL(1,𝔽25)—24no—
72C3×D3×C8—24no—
73#1816—31noSylow
74C2×C3×#41—31no—
75C2×#235C22×C311yescharacteristic
76C3×#131—34no—
77C3×#131—62no—
78C2×C3×M16—21no—
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16—61no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×M16C22×C311yescharacteristic
85C2×C3×M16C22×C311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—61no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C22×C311yescharacteristic
92C2×C4⋊Dic3C22×C311yescharacteristic
93C2×#208C22×C311yescharacteristic
94C22×C3⋊C8C22×C311yescharacteristic
95#907—22no—
96#907C3×C414yescomplemented
97C2×ΓL(1,𝔽25)—21no—
98C2×D3×C8—21no—
99C3×#108—62no—
100C3×#107—61no—
101C3×#107—61no—
102C3×#103—61no—
103C3×#103—61no—
104C3×#102—61no—
105C3×#102—61no—
106#822—22no—
107#821—21no—
108#816—21no—
109#810—21no—
110#809—21no—
111#807—21no—
112#807—21no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4—81no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C3×#67—22no—
124C3×#67—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C3×D12—21no—
129C3×D12C4⋊C412yes—
130C3×C4×D3—22no—
131C3×C4×D3—22no—
132C3×Dic6—21no—
133C3×Dic6C4⋊C412yes—
134C32×C8—22no—
135C32×C8—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8C22⋊C412yes—
138C3×C3⋊C8C22⋊C412yes—
139C2×#131—31no—
140C2×#108—31no—
141C2×#107—31no—
142#417—31no—
143#417—31no—
144#343—31no—
145#343C3×D311yescharacteristic, complemented
146C3×#41—32no—
147C3×#41—32no—
148C3×#41—61no—
149C3×#41—61no—
150C2×C3×Q8—31no—
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C23×C311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163#235—21no—
164#235—21no—
165#235C2×C3×C412yes—
166#235C3×Q812yes—
167C2×D12C3×D411yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6C3×D411yescharacteristic
170C3×M16—21no—
171C3×M16—21no—
172C3×M16—22no—
173C3×M16—21no—
174C3×M16—21no—
175C3×M16—21no—
176C3×M16—21no—
177C3×M16—22no—
178C3×M16—41no—
179C3×M16—41no—
180C3×M16—64no—
181C3×M16—61no—
182C3×M16—61no—
183C3×M16C4×D312yes—
184C3×M16C2×C3×C412yes—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—32no—
190C2×C3×C8—31no—
191C2×C3×C8—31no—
192C2×C3×C8—32no—
193C2×C3×C8—41no—
194C2×C3×C8—41no—
195C2×C3×C8—64no—
196C2×C3×C8—61no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207#208—21no—
208#208—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8C2×C3×C412yes—
211C2×C3⋊C8C3×D411yescharacteristic
212C2×C3⋊C8C3×D411yescharacteristic
213C2×C3⋊C8C3×D412yes—
214ΓL(1,𝔽25)—24no—
215D3×C8—24no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32#11711yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C2×C3×D3—22no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C32×C4—81no—
225C32×C4C2×C22⋊C411yescharacteristic
226C32×C4C2×C4⋊C411yescharacteristic
227C32×C4#12111yescharacteristic
228C32×C4C22⋊Q811yescharacteristic
229C3×Dic3—22no—
230C3×Dic3—81no—
231C2×#41—31no—
232#131—34no—
233#131—62no—
234C2×M16—31no—
235C2×M16—61no—
236C2×M16C2×C3×D311yescharacteristic
237C2×M16C2×C3×D311yescharacteristic
238C22×C8—31no—
239C22×C8—61no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4C2×C3×D311yescharacteristic
242#108—62no—
243#107—61no—
244#107—61no—
245#103—61no—
246#103—61no—
247#102—61no—
248#102—61no—
249C23×C3—21no—
250C23×C3—61no—
251C23×C3#23511yescharacteristic
252C23×C3C3×#4111yescharacteristic
253C22×D3—21no—
254C3×Q8—32no—
255C3×Q8—61no—
256C3×D4—32no—
257C3×D4—62no—
258C3×D4—62no—
259C3×D4—61no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—81no—
273C2×C3×C4—81no—
274C2×C3×C4—82no—
275C2×C3×C4—121no—
276C2×C3×C4—241no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×Q811yescharacteristic
283C2×C3×C4C22×C3×C411yescharacteristic
284C2×C3×C4C2×C3×D411yescharacteristic
285C2×C3×C4C2×C3×D411yescharacteristic
286C2×C3×C4C2×C3×D411yescharacteristic
287C2×C3×C4C2×C3×Q811yescharacteristic
288C2×C3×C4C3×#4111yescharacteristic
289#67—22no—
290#67—22no—
291C2×Dic3—21no—
292C2×Dic3—41no—
293C2×Dic3—81no—
294D12—21no—
295D12C3×C4⋊C412yes—
296C4×D3—22no—
297C4×D3—22no—
298Dic6—21no—
299Dic6C3×C4⋊C412yes—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—32no—
303C3×C8—32no—
304C3×C8—42no—
305C3×C8—42no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—121no—
309C3⋊C8—41no—
310C3⋊C8C3×C22⋊C412yes—
311C3⋊C8C3×C22⋊C412yes—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#38011yescharacteristic
315C2×C32#47211yescharacteristic
316C2×C32#47311yescharacteristic
317C3×D3—42no—
318#41—32no—
319#41—32no—
320#41—61no—
321#41—61no—
322C2×Q8—31no—
323C2×D4—31no—
324C2×D4—61no—
325C22×C4—21no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4C22×C3×D311yescharacteristic
329M16—21no—
330M16—21no—
331M16—21no—
332M16—64no—
333M16—61no—
334M16—61no—
335M16C3×C4×D312yes—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—32no—
339C2×C8—31no—
340C2×C8—31no—
341C2×C8—32no—
342C2×C8—64no—
343C2×C8—61no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—62no—
358C22×C3—121no—
359C22×C3—121no—
360C22×C3#87211yescharacteristic
361C22×C3#88411yescharacteristic
362C22×C3#89611yescharacteristic
363C22×C3C3×#11711yescharacteristic
364C22×C3C3×#12111yescharacteristic
365C22×C3C3×C22⋊Q811yescharacteristic
366C2×D3—22no—
367C2×D3—41no—
368C2×D3—41no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—62no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—241no—
378C3×C4D3×C22⋊C411yescharacteristic
379C3×C4#88411yescharacteristic
380C3×C4D3×C4⋊C411yescharacteristic
381C3×C4#89611yescharacteristic
382C3×C4C2×C3×C22⋊C411yescharacteristic
383C3×C4C2×C3×C4⋊C411yescharacteristic
384C3×C4C3×#12111yescharacteristic
385C3×C4C3×C22⋊Q811yescharacteristic
386Dic3—22no—
387Dic3—81no—
388C32#181611yescharacteristic, complemented, Sylow
389C23—61no—
390C23C3×#23511yescharacteristic
391Q8—32no—
392Q8—61no—
393D4—32no—
394D4—62no—
395D4—62no—
396D4—61no—
397C2×C4—41no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—81no—
402C2×C4—121no—
403C2×C4—241no—
404C2×C4C2×C3×C4×D311yescharacteristic
405C2×C4C3×#23511yescharacteristic
406C2×C4C3×D3×D411yescharacteristic
407C2×C4C3×D3×D411yescharacteristic
408C2×C4C3×D3×D411yescharacteristic
409C2×C4C3×D3×Q811yescharacteristic
410C8—22no—
411C8—32no—
412C8—32no—
413C8—41no—
414C8—121no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—122no—
425C2×C3#466711yescharacteristic
426C2×C3#474911yescharacteristic
427C2×C3#475511yescharacteristic
428C2×C3C3×#38011yescharacteristic
429C2×C3C3×#47211yescharacteristic
430C2×C3C3×#47311yescharacteristic
431D3—42no—
432C22—21no—
433C22—21no—
434C22—62no—
435C22—121no—
436C22—121no—
437C22C3×#87211yescharacteristic
438C22C3×#88411yescharacteristic
439C22C3×#89611yescharacteristic
440C4—62no—
441C4—81no—
442C4—241no—
443C4C3×D3×C22⋊C411yescharacteristic
444C4C3×#88411yescharacteristic
445C4C3×D3×C4⋊C411yescharacteristic
446C4C3×#89611yescharacteristic
447C3—21no—
448C3#6900111yescharacteristic, direct product factor
449C3C3×#181611yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—122no—
453C2C3×#466711yescharacteristic
454C2C3×#474911yescharacteristic
455C2C3×#475511yescharacteristic
subgroupG/H
centerC22×C3#884
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×#1816
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
3. C2×C3×#822C2semidirect
5. C2×C3×#807C2semidirect
6. C32×#343C2semidirect
7. C3×#4554C2semidirect
9. #69001C3direct (N × H)
18. C3×#907C4semidirect
35. C2×#822C2×C3semidirect
37. C2×#807C2×C3semidirect
40. C3×#343D3semidirect
41. C3×#343C2×C3semidirect
42. #4554C2×C3semidirect
96. #907C3×C4semidirect
145. #343C3×D3semidirect
388. C32#1816semidirect
448. C3#69001direct (N × H)
449. C3C3×#1816semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9072
C3×#51332
C2×C3×#8222
C3×#49662
C2×C3×#8072
C32×#3432
C3×#45542
C3×#18163
#690013