Finite Group Databasebeta

← C3×#70396 #11785537

Subgroups — C3×#70396 #11785537

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2C32×#421C211yesmaximal, characteristic
3C3×#5236C211yesmaximal, characteristic
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8C3×#1814—31nomaximal
9#70396C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C3×#948—21no—
14C3×#948—21no—
15C3×#948C412yescomplemented
16C3×#948C412yescomplemented
17C3×#926C2211yescharacteristic
18C2×C3×#208—21no—
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C32×#104—22no—
24C3×#837—22no—
25C3×#822—21no—
26C3×#822—21no—
27C3×#808—21no—
28C3×#807—21no—
29C2×C3×#131—31no—
30C2×#948C2×C311yescharacteristic
31C2×C3×#108—31no—
32C3×#427—31no—
33C3×#421—21no—
34C3×#421—31no—
35C3×#421D311yescharacteristic
36C3×#421C2×C311yescharacteristic
37#5236C2×C311yescharacteristic
38C2×#822C2×C311yescharacteristic, complemented
39#4998C2×C311yescharacteristic, complemented
40C3×#344—31no—
41C3×#344—31no—
42#4556C2×C311yescharacteristic, complemented
43#4533C2×C311yescharacteristic, complemented
44C32×#41—21no—
45C32×#41—21no—
46C32×#41C2×C412yes—
47C32×#41D412yes—
48C2×C32×Q8Q811yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4Q811yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C32×M16—21no—
54C32×M16—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—22no—
64C3×#208—22no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74C2×C3×C3⋊C8D411yescharacteristic
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77C2×C3×C3⋊C8D411yescharacteristic
78#1814—31noSylow
79C2×C3×#41—21no—
80C2×C3×#41C2×D311yescharacteristic
81C2×C3×#41C22×C311yescharacteristic
82C3×#131—32no—
83C3×#131—32no—
84C3×#131—61no—
85C3×#131—61no—
86C2×C3×M16—21no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—61no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C22×C311yescharacteristic
92C22×C3×C8—31no—
93C22×C3×C8—61no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C22×C311yescharacteristic
98#948—21no—
99#948—21no—
100#948C3×C412yescomplemented
101#948C3×C412yescomplemented
102#926C22×C311yescharacteristic
103C2×#208—21no—
104C2×#208C22×C311yescharacteristic
105C2×#208C22×C311yescharacteristic
106C22×C3⋊C8—21no—
107C22×C3⋊C8C22×C311yescharacteristic
108C3×#108—61no—
109C3×#108—61no—
110C3×#107—61no—
111C3×#106—61no—
112C3×#104—24no—
113C3×#104—22no—
114C3×#104—22no—
115C3×#104—62no—
116#837—22no—
117#822—21no—
118#822—21no—
119#808—21no—
120#807—21no—
121C23×C32—21no—
122C23×C32#4111yescharacteristic
123C32×Q8—21no—
124C32×Q8C4⋊C412yes—
125C32×D4—22no—
126C32×D4—22no—
127C32×D4—21no—
128C32×D4C4⋊C412yes—
129C2×C32×C4—21no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
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—41no—
140C32×C8—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8C22⋊C411yescharacteristic
144C3×C3⋊C8C22⋊C411yescharacteristic
145C3×C3⋊C8C22⋊C411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C2×#131—31no—
148C2×#108—31no—
149#427—31no—
150#421—31no—
151#421C3×D311yescharacteristic
152#344—31no—
153#344—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×#41C4×D312yes—
163C3×#41#6712yes—
164C3×#41C2×C3×C412yes—
165C3×#41C3×D412yes—
166C2×C3×Q8—21no—
167C2×C3×Q8Dic611yescharacteristic
168C2×C3×Q8C3×Q811yescharacteristic
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—41no—
173C2×C3×D4Dic611yescharacteristic
174C2×C3×D4C3×Q811yescharacteristic
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—41no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C3×M16—22no—
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—32no—
187C3×M16—41no—
188C3×M16—62no—
189C3×M16—62no—
190C3×M16—61no—
191C3×M16—61no—
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—31no—
200C2×C3×C8—31no—
201C2×C3×C8—41no—
202C2×C3×C8—62no—
203C2×C3×C8—62no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—41no—
213C3×C22⋊C4—61no—
214C3×C42—22no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—61no—
218#217—21no—
219C4⋊Dic3—21no—
220C4×Dic3—21no—
221#208—21no—
222#208—22no—
223#208—22no—
224#208—21no—
225#208—21no—
226#208C2×C3×C412yes—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—22no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8C2×C3×C411yescharacteristic
232C2×C3⋊C8C2×C3×C411yescharacteristic
233C2×C3⋊C8C3×D411yescharacteristic
234C2×C3⋊C8C3×D411yescharacteristic
235C2×C3⋊C8C3×D411yescharacteristic
236C2×C3⋊C8C3×D411yescharacteristic
237C22×C32—22no—
238C22×C32—41no—
239C22×C32—42no—
240C22×C32#11711yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32C22⋊Q811yescharacteristic
243C32×C4—22no—
244C32×C4—81no—
245C32×C4C2×C22⋊C411yescharacteristic
246C32×C4C2×C4⋊C411yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C3×Dic3—81no—
250C2×#41C2×C3×D311yescharacteristic
251#131—32no—
252#131—32no—
253#131—61no—
254#131—61no—
255C2×M16—31no—
256C2×M16—31no—
257C2×M16—61no—
258C2×M16C2×C3×D311yescharacteristic
259C22×C8—31no—
260C22×C8—61no—
261#117—31no—
262#117C2×C3×D311yescharacteristic
263#108—61no—
264#108—61no—
265#107—61no—
266#106—61no—
267#104—22no—
268#104—62no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—41no—
273C23×C3#23711yescharacteristic
274C23×C3C3×#4111yescharacteristic
275C3×Q8—21no—
276C3×Q8—21no—
277C3×Q8—22no—
278C3×Q8—41no—
279C3×Q8Dic3⋊C412yes—
280C3×Q8C3×C4⋊C412yes—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—21no—
286C3×D4—21no—
287C3×D4—22no—
288C3×D4—41no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4Dic3⋊C412yes—
292C3×D4C3×C4⋊C412yes—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—121no—
312C2×C3×C4C2×Dic611yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C22×C3×C411yescharacteristic
319C2×C3×C4C2×C3×D411yescharacteristic
320C2×C3×C4C2×C3×D411yescharacteristic
321C2×C3×C4C2×C3×D411yescharacteristic
322C2×C3×C4C2×C3×Q811yescharacteristic
323C2×C3×C4C3×#4111yescharacteristic
324C2×Dic3—41no—
325C3×C8—31no—
326C3×C8—31no—
327C3×C8—31no—
328C3×C8—31no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3×C8—62no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8C3×C22⋊C411yescharacteristic
337C3⋊C8C3×C22⋊C411yescharacteristic
338C3⋊C8C3×C22⋊C411yescharacteristic
339C3⋊C8C3×C22⋊C411yescharacteristic
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—42no—
344C2×C32#38011yescharacteristic
345#41—21no—
346#41—21no—
347#41C3×C4×D312yes—
348#41C3×#6712yes—
349C2×Q8C3×Dic611yescharacteristic
350C2×D4—21no—
351C2×D4C3×Dic611yescharacteristic
352C22×C4—21no—
353C22×C4C22×C3×D311yescharacteristic
354M16—21no—
355M16—21no—
356M16—32no—
357M16—62no—
358M16—62no—
359M16—61no—
360M16—61no—
361M16—61no—
362C2×C8—21no—
363C2×C8—31no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8—31no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—62no—
370C2×C8—62no—
371C2×C8—61no—
372C2×C8—61no—
373C4⋊C4—21no—
374C4⋊C4—61no—
375C22⋊C4—21no—
376C22⋊C4—61no—
377C42—21no—
378C42—61no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—42no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—81no—
390C22×C3—82no—
391C22×C3#87711yescharacteristic
392C22×C3#87811yescharacteristic
393C22×C3#93911yescharacteristic
394C22×C3C3×#11711yescharacteristic
395C22×C3C3×#12111yescharacteristic
396C22×C3C3×C22⋊Q811yescharacteristic
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—42no—
404C3×C4—81no—
405C3×C4—81no—
406C3×C4—82no—
407C3×C4—241no—
408C3×C4#87811yescharacteristic
409C3×C4D3×C22⋊C411yescharacteristic
410C3×C4C2×Dic3⋊C411yescharacteristic
411C3×C4#93911yescharacteristic
412C3×C4C2×C3×C22⋊C411yescharacteristic
413C3×C4C2×C3×C4⋊C411yescharacteristic
414C3×C4C3×#12111yescharacteristic
415C3×C4C3×C22⋊Q811yescharacteristic
416Dic3—81no—
417C32#181411yescharacteristic, complemented, Sylow
418C23—21no—
419C23C3×#23711yescharacteristic
420Q8—21no—
421Q8C3×Dic3⋊C412yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4C3×Dic3⋊C412yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—121no—
431C2×C4C2×C3×Dic611yescharacteristic
432C2×C4C2×C3×C4×D311yescharacteristic
433C2×C4C3×D3×D411yescharacteristic
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C3×#23711yescharacteristic
436C2×C4C2×C3×#6711yescharacteristic
437C8—31no—
438C8—31no—
439C8—31no—
440C8—31no—
441C8—41no—
442C8—62no—
443C8—121no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3—42no—
455C2×C3—42no—
456C2×C3—82no—
457C2×C3#494211yescharacteristic
458C2×C3C3×#38011yescharacteristic
459C22—22no—
460C22—41no—
461C22—42no—
462C22C3×#87711yescharacteristic
463C22C3×#87811yescharacteristic
464C22C3×#93911yescharacteristic
465C4—22no—
466C4—81no—
467C4—241no—
468C4C3×#87811yescharacteristic
469C4C3×D3×C22⋊C411yescharacteristic
470C4C2×C3×Dic3⋊C411yescharacteristic
471C4C3×#93911yescharacteristic
472C3—21no—
473C3#7039611yescharacteristic, direct product factor
474C3C3×#181411yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—21no—
478C2—42no—
479C2C3×#494211yescharacteristic
subgroupG/H
centerC3×C4#939
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#421C2
socleC2×C32#380
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#421D3
hypocenterC3C3×#1814
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
4. C2×C3×#822C2semidirect
5. C3×#4998C2semidirect
6. C3×#4556C2semidirect
7. C3×#4533C2semidirect
9. #70396C3direct (N × H)
15. C3×#948C4semidirect
16. C3×#948C4semidirect
38. C2×#822C2×C3semidirect
39. #4998C2×C3semidirect
42. #4556C2×C3semidirect
43. #4533C2×C3semidirect
100. #948C3×C4semidirect
101. #948C3×C4semidirect
417. C32#1814semidirect
473. C3#70396direct (N × H)
474. C3C3×#1814semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
C32×#4212
C3×#52362
C2×C3×#8222
C3×#49982
C3×#45562
C3×#45332
C3×#18143
#703963