Finite Group Databasebeta

← C3×#69012 #11789695

Subgroups — C3×#69012 #11789695

Order 1152.

477 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#825C211yesmaximal, characteristic
2C3×#5132C211yesmaximal, characteristic
3C3×#5124C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic
6C32×#344C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1932—31nomaximal
9#69012C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#825—21no—
18C3×#825—21no—
19C3×#824C412yescomplemented
20C3×#823C412yescomplemented
21C3×#822—22no—
22C3×#815—21no—
23C3×C8×Dic3—21no—
24C3×#805—22no—
25C3×#430—31no—
26C3×#421—31no—
27C2×C3×#104—31no—
28C3×#413—31no—
29C3×C4×M16—31no—
30C2×#825C2×C311yescharacteristic
31#5132C2×C311yescharacteristic
32#5124C2×C311yescharacteristic, complemented
33Dic3×M16C2×C311yescharacteristic, complemented
34#5005C2×C311yescharacteristic
35C3×#344—21no—
36C3×#344D311yescharacteristic, complemented
37C3×#344C2×C311yescharacteristic, complemented
38C3×#339—31no—
39#4532C2×C311yescharacteristic, complemented
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—21no—
42C22×C3×Dic3—21no—
43C3×#235—21no—
44C3×#235—21no—
45C3×#235—21no—
46C3×#235—21no—
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C32×M16—21no—
51C32×M16—21no—
52C32×M16—21no—
53C32×M16C2×C412yes—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208C2×C412yes—
65C3×#208D412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68#1932—31noSylow
69C2×C3×#41—31no—
70C2×#235C22×C311yescharacteristic
71C2×C3×M16—21no—
72C2×C3×M16—21no—
73C2×C3×M16—31no—
74C2×C3×M16—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C2×C3×M16C22×C311yescharacteristic
79C3×#117—21no—
80C3×#117C2×D311yescharacteristic
81C3×#117C22×C311yescharacteristic
82C2×C3×C42—31no—
83C2×C4×Dic3C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C2×#208C22×C311yescharacteristic
86C3×#108—62no—
87C3×#104—62no—
88C3×#104—61no—
89C3×#104—61no—
90C3×#101—32no—
91C3×#100—32no—
92C3×#97—61no—
93C3×C4×C8—61no—
94#825—21no—
95#825—21no—
96#824C3×C412yescomplemented
97#823C3×C412yescomplemented
98#822—22no—
99#815—21no—
100C8×Dic3—21no—
101#805—22no—
102C23×C32#4111yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—41no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C3×#67—41no—
112C3×#67—41no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—42no—
117C3×D12—21no—
118C3×D12—21no—
119C3×C4×D3—41no—
120C3×C4×D3—41no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C32×C8—22no—
124C32×C8—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127#430—31no—
128#421—31no—
129C2×#104—31no—
130#413—31no—
131C4×M16—31no—
132#344C3×D311yescharacteristic, complemented
133#339—31no—
134C3×#41—61no—
135C3×#41—61no—
136C3×#41—61no—
137C3×#41—61no—
138C2×C3×Q8—31no—
139C2×C3×D4—31no—
140C2×C3×D4—61no—
141C22×C3×C4—21no—
142C22×C3×C4—61no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C23×C311yescharacteristic
146C2×#67—21no—
147C22×Dic3—21no—
148#235—21no—
149#235—21no—
150#235—21no—
151#235—21no—
152C2×D12C2×C3×C411yescharacteristic
153C2×C4×D3—21no—
154C2×Dic6C2×C3×C411yescharacteristic
155C3×M16—21no—
156C3×M16—21no—
157C3×M16—21no—
158C3×M16—21no—
159C3×M16—21no—
160C3×M16—21no—
161C3×M16—22no—
162C3×M16—32no—
163C3×M16—32no—
164C3×M16—41no—
165C3×M16—41no—
166C3×M16—41no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16C4×D312yes—
170C3×M16C2×C3×C412yes—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—22no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—41no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—41no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—41no—
190C3×C42—61no—
191C4×Dic3—21no—
192C4×Dic3C3×D411yescharacteristic
193C4×Dic3C3×D411yescharacteristic
194#208—21no—
195#208—21no—
196#208C2×C3×C412yes—
197#208C3×D412yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C22×C32—41no—
201C22×C32#11711yescharacteristic
202C22×C32#12311yescharacteristic
203C22×C32#12411yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—81no—
206C32×C4—81no—
207C32×C4C4×D411yescharacteristic
208C32×C4C4×D411yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12611yescharacteristic
211C3×Dic3—22no—
212C3×Dic3—41no—
213C3×Dic3—41no—
214C2×#41—31no—
215C2×M16—31no—
216C2×M16—31no—
217C2×M16C2×C3×D311yescharacteristic
218C2×M16C2×C3×D311yescharacteristic
219#117C2×C3×D311yescharacteristic
220C2×C42—31no—
221#108—62no—
222#104—62no—
223#104—61no—
224#104—61no—
225#101—32no—
226#100—32no—
227#97—61no—
228C4×C8—61no—
229C23×C3—21no—
230C23×C3—61no—
231C23×C3#23511yescharacteristic
232C23×C3C3×#4111yescharacteristic
233C22×D3—21no—
234C3×Q8—61no—
235C3×Q8—61no—
236C3×D4—61no—
237C3×D4—61no—
238C3×D4—121no—
239C3×D4—121no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—42no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—122no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4C2×C4×D311yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23911yescharacteristic
261C2×C3×C4C22×C3×C411yescharacteristic
262C2×C3×C4C2×C3×D411yescharacteristic
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C3×#4111yescharacteristic
265C2×C3×C4C3×#4111yescharacteristic
266C2×C3×C4C3×#4111yescharacteristic
267#67—41no—
268#67—41no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—42no—
273D12—21no—
274D12—21no—
275C4×D3—41no—
276C4×D3—41no—
277Dic6—21no—
278Dic6—21no—
279C3×C8—22no—
280C3×C8—22no—
281C3×C8—42no—
282C3×C8—42no—
283C3×C8—41no—
284C3×C8—41no—
285C3×C8—62no—
286C3×C8—62no—
287C3⋊C8—22no—
288C3⋊C8—22no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32#38811yescharacteristic
293C3×D3—81no—
294#41—61no—
295#41—61no—
296#41—61no—
297#41—61no—
298C2×Q8—31no—
299C2×D4—31no—
300C2×D4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4C22×C3×D311yescharacteristic
304M16—21no—
305M16—21no—
306M16—21no—
307M16—32no—
308M16—32no—
309M16—61no—
310M16—61no—
311M16C3×C4×D312yes—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—61no—
315C2×C8—61no—
316C4⋊C4—21no—
317C22⋊C4—21no—
318C42—21no—
319C42—31no—
320C42—31no—
321C42—61no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—121no—
329C22×C3—241no—
330C22×C3#87211yescharacteristic
331C22×C3#88511yescharacteristic
332C22×C3#89411yescharacteristic
333C22×C3C3×#11711yescharacteristic
334C22×C3C3×#12311yescharacteristic
335C22×C3C3×#12411yescharacteristic
336C2×D3—41no—
337C2×D3—81no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—62no—
343C3×C4—81no—
344C3×C4—81no—
345C3×C4—82no—
346C3×C4—121no—
347C3×C4—121no—
348C3×C4#67⋊C411yescharacteristic
349C3×C4#88411yescharacteristic
350C3×C4#89311yescharacteristic
351C3×C4#89811yescharacteristic
352C3×C4C3×C4×D411yescharacteristic
353C3×C4C3×C4×D411yescharacteristic
354C3×C4C3×#12111yescharacteristic
355C3×C4C3×#12611yescharacteristic
356Dic3—22no—
357Dic3—41no—
358Dic3—41no—
359C32#193211yescharacteristic, complemented, Sylow
360C23—61no—
361C23C3×#23511yescharacteristic
362Q8—61no—
363Q8—61no—
364D4—61no—
365D4—61no—
366D4—121no—
367D4—121no—
368C2×C4—41no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—122no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4C2×C3×C4×D311yescharacteristic
376C2×C4C3×#23511yescharacteristic
377C2×C4C3×D3×D411yescharacteristic
378C2×C4C3×D3×D411yescharacteristic
379C2×C4C3×#23711yescharacteristic
380C2×C4C3×#23911yescharacteristic
381C8—22no—
382C8—41no—
383C8—62no—
384C8—62no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—241no—
396C2×C3#466911yescharacteristic
397C2×C3C3×#38811yescharacteristic
398D3—81no—
399C22—41no—
400C22—121no—
401C22—241no—
402C22C3×#87211yescharacteristic
403C22C3×#88511yescharacteristic
404C22C3×#89411yescharacteristic
405C4—62no—
406C4—81no—
407C4—121no—
408C4—121no—
409C4C3×#67⋊C411yescharacteristic
410C4C3×#88411yescharacteristic
411C4C3×#89311yescharacteristic
412C4C3×#89811yescharacteristic
413C3—21no—
414C3#6901211yescharacteristic, direct product factor
415C3C3×#193211yescharacteristic, complemented
416C2—21no—
417C2—21no—
418C2—21no—
419C2—241no—
420C2C3×#466911yescharacteristic
subgroupG/H
centerC3×C4#884
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#344D3
hypocenterC3C3×#1932
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
3. C3×#5124C2semidirect
4. C3×Dic3×M16C2semidirect
6. C32×#344C2semidirect
7. C3×#4532C2semidirect
9. #69012C3direct (N × H)
19. C3×#824C4semidirect
20. C3×#823C4semidirect
32. #5124C2×C3semidirect
33. Dic3×M16C2×C3semidirect
36. C3×#344D3semidirect
37. C3×#344C2×C3semidirect
39. #4532C2×C3semidirect
96. #824C3×C4semidirect
97. #823C3×C4semidirect
132. #344C3×D3semidirect
359. C32#1932semidirect
414. C3#69012direct (N × H)
415. C3C3×#1932semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8252
C3×#51322
C3×#51242
C3×Dic3×M162
C3×#50052
C32×#3442
C3×#45322
C3×#19323
#690123