Finite Group Databasebeta

← C3×#70376 #11787010

Subgroups — C3×#70376 #11787010

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C3×#5119C211yesmaximal, characteristic, complemented
6C3×#4524C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1866—31nomaximal
9#70376C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C3×#948—22no—
14C3×#948—22no—
15C3×#926C2211yescharacteristic
16C2×C3×#208—21no—
17C2×C3×#208C2211yescharacteristic
18C22×C3×C3⋊C8—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C32×#104—22no—
22C3×#835C411yescharacteristic, complemented
23C3×#835C411yescharacteristic, complemented
24C3×#832C411yescharacteristic, complemented
25C3×#832C411yescharacteristic, complemented
26C3×#822—22no—
27C3×Dic3⋊C8—21no—
28C3×Dic3⋊C8—21no—
29C2×C3×#131—31no—
30C2×#948C2×C311yescharacteristic
31C2×C3×#108—31no—
32C3×#424—31no—
33C2×C3×#104—21no—
34C2×C3×#104D311yescharacteristic
35C2×C3×#104C2×C311yescharacteristic
36C3×#416—31no—
37#5233C2×C311yescharacteristic
38C2×#822C2×C311yescharacteristic, complemented
39#5119C2×C311yescharacteristic, complemented
40C3×#339—31no—
41C3×#336—31no—
42#4524C2×C311yescharacteristic, complemented
43#4523C2×C311yescharacteristic, complemented
44C32×#41—21no—
45C32×#41—21no—
46C32×#41D412yes—
47C32×#41Q812yes—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C32×M16—21no—
55C32×M16—21no—
56C2×C32×C8—21no—
57C32×C42—21no—
58C32×C42—21no—
59C3×#217—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×C4×Dic3—21no—
63C3×#208—24no—
64C3×#208—21no—
65C3×#208D412yes—
66C2×C3×C3⋊C8—24no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75C2×C3×C3⋊C8D411yescharacteristic
76#1866—31noSylow
77C2×C3×#41—21no—
78C2×C3×#41C2×D311yescharacteristic
79C2×C3×#41C22×C311yescharacteristic
80C3×#131—62no—
81C3×#131—62no—
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16—61no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C22×C311yescharacteristic
87C22×C3×C8—31no—
88C22×C3×C8—31no—
89C22×C3×C8—61no—
90C3×#117—31no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C22×C311yescharacteristic
94#948—22no—
95#948—22no—
96#926C22×C311yescharacteristic
97C2×#208—21no—
98C2×#208C22×C311yescharacteristic
99C22×C3⋊C8—21no—
100C22×C3⋊C8C22×C311yescharacteristic
101C22×C3⋊C8C22×C311yescharacteristic
102C3×#108—62no—
103C3×C4⋊C8—61no—
104C3×C4⋊C8—61no—
105C3×#104—24no—
106C3×#104—22no—
107C3×#104—22no—
108C3×#103—31no—
109C3×#103—31no—
110C3×#102—31no—
111C3×#102—31no—
112#835C3×C411yescharacteristic, complemented
113#835C3×C411yescharacteristic, complemented
114#832C3×C411yescharacteristic, complemented
115#832C3×C411yescharacteristic, complemented
116#822—22no—
117Dic3⋊C8—21no—
118Dic3⋊C8—21no—
119C23×C32—21no—
120C23×C32#4111yescharacteristic
121C32×Q8—21no—
122C32×Q8C4⋊C412yes—
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—21no—
126C32×D4C4⋊C412yes—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×Q811yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C32×C8—41no—
142C3×C3⋊C8—21no—
143C3×C3⋊C8—21no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—21no—
147C2×#131—31no—
148C2×#108—31no—
149#424—31no—
150C2×#104C3×D311yescharacteristic
151#416—31no—
152#339—31no—
153#336—31no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—22no—
159C3×#41—22no—
160C3×#41—41no—
161C3×#41—41no—
162C3×#41Dic612yes—
163C3×#41#6712yes—
164C3×#41C3×D412yes—
165C3×#41C3×Q812yes—
166C2×C3×Q8—21no—
167C2×C3×Q8C4×D311yescharacteristic
168C2×C3×Q8C2×C3×C411yescharacteristic
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4C4×D311yescharacteristic
174C2×C3×D4C2×C3×C411yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—41no—
181C22×C3×C4—41no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C23×C311yescharacteristic
184C3×M16—22no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—32no—
190C3×M16—41no—
191C3×M16—64no—
192C3×M16—61no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—41no—
200C2×C3×C8—64no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C3×C4⋊C4—31no—
207C3×C4⋊C4—31no—
208C3×C22⋊C4—61no—
209C3×C42—22no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—41no—
215C3×C42—61no—
216#217—21no—
217C4⋊Dic3C2×C3×C411yescharacteristic
218C4⋊Dic3C2×C3×C411yescharacteristic
219C4×Dic3—21no—
220#208—24no—
221#208—21no—
222#208C3×D412yes—
223C2×C3⋊C8—24no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C2×C3×C411yescharacteristic
230C2×C3⋊C8C2×C3×C411yescharacteristic
231C2×C3⋊C8C3×D411yescharacteristic
232C2×C3⋊C8C3×D411yescharacteristic
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—22no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32C4×D411yescharacteristic
239C22×C32C22⋊Q811yescharacteristic
240C22×C32#12311yescharacteristic
241C32×C4—22no—
242C32×C4—42no—
243C32×C4C2×C4⋊C411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4#12011yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C3×Dic3—41no—
248C3×Dic3—41no—
249C2×#41C2×C3×D311yescharacteristic
250#131—62no—
251#131—62no—
252C2×M16—31no—
253C2×M16—61no—
254C2×M16C2×C3×D311yescharacteristic
255C22×C8—31no—
256C22×C8—31no—
257C22×C8—61no—
258#117—31no—
259C2×C42C2×C3×D311yescharacteristic
260#108—62no—
261C4⋊C8—61no—
262C4⋊C8—61no—
263#104—22no—
264#103—31no—
265#103—31no—
266#102—31no—
267#102—31no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—41no—
272C23×C3#23711yescharacteristic
273C23×C3C3×#4111yescharacteristic
274C3×Q8—21no—
275C3×Q8—21no—
276C3×Q8—22no—
277C3×Q8—41no—
278C3×Q8Dic3⋊C412yes—
279C3×Q8C3×C4⋊C412yes—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—22no—
287C3×D4—41no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4Dic3⋊C412yes—
291C3×D4C3×C4⋊C412yes—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—42no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4C2×Dic611yescharacteristic
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C22×C3×C411yescharacteristic
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×C3×C4C2×C3×D411yescharacteristic
328C2×C3×C4C2×C3×Q811yescharacteristic
329C2×C3×C4C3×#4111yescharacteristic
330C2×Dic3—21no—
331C2×Dic3—21no—
332C3×C8—42no—
333C3×C8—41no—
334C3×C8—41no—
335C3×C8—61no—
336C3×C8—61no—
337C3×C8—61no—
338C3×C8—61no—
339C3×C8—62no—
340C3⋊C8—21no—
341C3⋊C8—21no—
342C3⋊C8—21no—
343C3⋊C8—22no—
344C3⋊C8—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—42no—
348C2×C32#38511yescharacteristic
349C2×C32#44311yescharacteristic
350C2×C32#44411yescharacteristic
351#41—21no—
352#41—21no—
353#41C3×Dic612yes—
354#41C3×#6712yes—
355C2×Q8C3×C4×D311yescharacteristic
356C2×D4—21no—
357C2×D4C3×C4×D311yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4C22×C3×D311yescharacteristic
361M16—21no—
362M16—21no—
363M16—32no—
364M16—64no—
365M16—61no—
366C2×C8—21no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—31no—
370C2×C8—31no—
371C2×C8—64no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—61no—
377C4⋊C4—31no—
378C4⋊C4—31no—
379C22⋊C4—61no—
380C42—21no—
381C42—21no—
382C42—61no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—81no—
400C22×C3—81no—
401C22×C3#87811yescharacteristic
402C22×C3#67⋊C411yescharacteristic
403C22×C3#93511yescharacteristic
404C22×C3C3×C4×D411yescharacteristic
405C22×C3C3×C22⋊Q811yescharacteristic
406C22×C3C3×#12311yescharacteristic
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—42no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—44no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4#87811yescharacteristic
420C3×C4#67⋊C411yescharacteristic
421C3×C4C2×Dic3⋊C411yescharacteristic
422C3×C4#93711yescharacteristic
423C3×C4C2×C3×C4⋊C411yescharacteristic
424C3×C4C3×C4×D411yescharacteristic
425C3×C4C3×#12011yescharacteristic
426C3×C4C3×C22⋊Q811yescharacteristic
427Dic3—41no—
428Dic3—41no—
429C32#186611yescharacteristic, complemented, Sylow
430C23—21no—
431C23C3×#23711yescharacteristic
432Q8—21no—
433Q8C3×Dic3⋊C412yes—
434D4—22no—
435D4—22no—
436D4—21no—
437D4C3×Dic3⋊C412yes—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4C2×C3×Dic611yescharacteristic
447C2×C4C2×C3×C4×D311yescharacteristic
448C2×C4C3×D3×D411yescharacteristic
449C2×C4C3×D3×D411yescharacteristic
450C2×C4C3×#23711yescharacteristic
451C2×C4C2×C3×#6711yescharacteristic
452C8—41no—
453C8—61no—
454C8—61no—
455C8—61no—
456C8—61no—
457C8—62no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—42no—
468C2×C3—42no—
469C2×C3—82no—
470C2×C3#482311yescharacteristic
471C2×C3#482411yescharacteristic
472C2×C3#494611yescharacteristic
473C2×C3C3×#38511yescharacteristic
474C2×C3C3×#44311yescharacteristic
475C2×C3C3×#44411yescharacteristic
476C22—21no—
477C22—21no—
478C22—22no—
479C22—41no—
480C22—41no—
481C22C3×#87811yescharacteristic
482C22C3×#67⋊C411yescharacteristic
483C22C3×#93511yescharacteristic
484C4—22no—
485C4—42no—
486C4—121no—
487C4—121no—
488C4C3×#87811yescharacteristic
489C4C3×#67⋊C411yescharacteristic
490C4C2×C3×Dic3⋊C411yescharacteristic
491C4C3×#93711yescharacteristic
492C3—21no—
493C3#7037611yescharacteristic, direct product factor
494C3C3×#186611yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—42no—
498C2C3×#482311yescharacteristic
499C2C3×#482411yescharacteristic
500C2C3×#494611yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C4×D4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1866
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
4. C2×C3×#822C2semidirect
5. C3×#5119C2semidirect
6. C3×#4524C2semidirect
7. C3×#4523C2semidirect
9. #70376C3direct (N × H)
22. C3×#835C4semidirect
23. C3×#835C4semidirect
24. C3×#832C4semidirect
25. C3×#832C4semidirect
38. C2×#822C2×C3semidirect
39. #5119C2×C3semidirect
42. #4524C2×C3semidirect
43. #4523C2×C3semidirect
112. #835C3×C4semidirect
113. #835C3×C4semidirect
114. #832C3×C4semidirect
115. #832C3×C4semidirect
429. C32#1866semidirect
493. C3#70376direct (N × H)
494. C3C3×#1866semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
C2×C32×#1042
C3×#52332
C2×C3×#8222
C3×#51192
C3×#45242
C3×#45232
C3×#18663
#703763