Finite Group Databasebeta

← C3×#69874 #11789701

Subgroups — C3×#69874 #11789701

Order 1152.

503 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×M16C211yesmaximal, characteristic, complemented
2C3×#5139C211yesmaximal, characteristic
3C3×#5132C211yesmaximal, characteristic
4C3×#5124C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic
6C3×#4559C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1932—31nomaximal
9#69874C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#97—21no—
18C32×C4×C8—21no—
19C3×#825—22no—
20C3×#824C412yescomplemented
21C3×#823C412yescomplemented
22C3×#822—22no—
23C3×#805—21no—
24C3×#805—21no—
25C3×#430—31no—
26C3×#421—31no—
27C2×C3×#104—31no—
28C3×#413—31no—
29C3×C4×M16—21no—
30C3×C4×M16D311yescharacteristic, complemented
31C3×C4×M16C2×C311yescharacteristic, complemented
32#5139C2×C311yescharacteristic
33#5132C2×C311yescharacteristic
34#5124C2×C311yescharacteristic, complemented
35C2×#805C2×C311yescharacteristic
36C3×#344—31no—
37C3×#339—31no—
38#4559C2×C311yescharacteristic, complemented
39#4523C2×C311yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—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×M16C2×C412yes—
53C32×M16D412yes—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C42—21no—
57C32×C42D411yescharacteristic
58C32×C42D411yescharacteristic
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208C2×C412yes—
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—31no—
80C2×C3×C42—21no—
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C22×C311yescharacteristic
83#926C22×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—22no—
93C3×#97—21no—
94C3×#97—21no—
95C3×C4×C8—22no—
96C3×C4×C8—21no—
97C3×C4×C8—21no—
98#825—22no—
99#824C3×C412yescomplemented
100#823C3×C412yescomplemented
101#822—22no—
102#805—21no—
103#805—21no—
104C23×C32#4111yescharacteristic
105C22×C3×D3—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4—42no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C3×#67—41no—
116C3×#67—41no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—41no—
119C3×D12—21no—
120C3×D12—21no—
121C3×C4×D3—41no—
122C3×C4×D3—41no—
123C3×Dic6—21no—
124C3×Dic6—21no—
125C32×C8—22no—
126C32×C8—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#430—31no—
130#421—31no—
131C2×#104—31no—
132#413—31no—
133C4×M16C3×D311yescharacteristic, complemented
134#344—31no—
135#339—31no—
136C3×#41—61no—
137C3×#41—61no—
138C3×#41—61no—
139C3×#41—61no—
140C2×C3×Q8—31no—
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C23×C311yescharacteristic
150C2×#67—21no—
151#235—21no—
152#235—21no—
153#235—21no—
154#235—21no—
155C2×D12C2×C3×C411yescharacteristic
156C2×C4×D3—21no—
157C2×Dic6C2×C3×C411yescharacteristic
158C3×M16—22no—
159C3×M16—22no—
160C3×M16—21no—
161C3×M16—21no—
162C3×M16—21no—
163C3×M16—21no—
164C3×M16—22no—
165C3×M16—22no—
166C3×M16—32no—
167C3×M16—61no—
168C3×M16—61no—
169C3×M16—61no—
170C3×M16C4×D312yes—
171C3×M16D1212yes—
172C3×M16C2×C3×C412yes—
173C3×M16C3×D412yes—
174C2×C3×C8—22no—
175C2×C3×C8—22no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C42—22no—
185C3×C42—21no—
186C3×C42—21no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—61no—
190C3×C42#6711yescharacteristic
191C3×C42#6711yescharacteristic
192C3×C42C3×D411yescharacteristic
193C3×C42C3×D411yescharacteristic
194#217—21no—
195C4⋊Dic3—21no—
196C4×Dic3—21no—
197#208—21no—
198#208—21no—
199#208—21no—
200#208C2×C3×C412yes—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C22×C32—41no—
204C22×C32#11711yescharacteristic
205C22×C32#12311yescharacteristic
206C22×C32#12411yescharacteristic
207C2×C3×D3—41no—
208C2×C3×D3—81no—
209C32×C4—22no—
210C32×C4—41no—
211C32×C4C4×D411yescharacteristic
212C32×C4C4×D411yescharacteristic
213C32×C4#12111yescharacteristic
214C32×C4#12611yescharacteristic
215C3×Dic3—41no—
216C3×Dic3—81no—
217C2×#41—31no—
218C2×M16—31no—
219C2×M16—31no—
220C2×M16C2×C3×D311yescharacteristic
221C2×M16C2×C3×D311yescharacteristic
222#117—31no—
223C2×C42C2×C3×D311yescharacteristic
224#108—62no—
225#104—62no—
226#104—61no—
227#104—61no—
228#101—32no—
229#100—32no—
230#97—21no—
231C4×C8—21no—
232C23×C3—21no—
233C23×C3—61no—
234C23×C3#23511yescharacteristic
235C23×C3C3×#4111yescharacteristic
236C22×D3—21no—
237C3×Q8—61no—
238C3×Q8—61no—
239C3×D4—61no—
240C3×D4—61no—
241C3×D4—121no—
242C3×D4—121no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—61no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4—121no—
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C22×C3×C411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270C2×C3×C4C2×C3×D411yescharacteristic
271C2×C3×C4C3×#4111yescharacteristic
272C2×C3×C4C3×#4111yescharacteristic
273C2×C3×C4C3×#4111yescharacteristic
274#67—41no—
275#67—41no—
276C2×Dic3—21no—
277C2×Dic3—41no—
278D12—21no—
279D12—21no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—21no—
283Dic6—21no—
284C3×C8—24no—
285C3×C8—24no—
286C3×C8—22no—
287C3×C8—22no—
288C3×C8—22no—
289C3×C8—22no—
290C3×C8—62no—
291C3×C8—121no—
292C3⋊C8—22no—
293C3⋊C8—41no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32#38811yescharacteristic
298C3×D3—81no—
299#41—61no—
300#41—61no—
301#41—61no—
302#41—61no—
303C2×Q8—31no—
304C2×D4—31no—
305C2×D4—61no—
306C22×C4—21no—
307C22×C4—61no—
308C22×C4C22×C3×D311yescharacteristic
309M16—21no—
310M16—21no—
311M16—32no—
312M16—61no—
313M16—61no—
314M16—61no—
315M16C3×C4×D312yes—
316M16C3×D1212yes—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—61no—
320C2×C8—61no—
321C4⋊C4—61no—
322C22⋊C4—61no—
323C42—21no—
324C42—61no—
325C42C3×#6711yescharacteristic
326C42C3×#6711yescharacteristic
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—42no—
333C22×C3—121no—
334C22×C3—241no—
335C22×C3#87211yescharacteristic
336C22×C3#87511yescharacteristic
337C22×C3#92911yescharacteristic
338C22×C3C3×#11711yescharacteristic
339C22×C3C3×#12311yescharacteristic
340C22×C3C3×#12411yescharacteristic
341C2×D3—41no—
342C2×D3—81no—
343C3×C4—24no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—42no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—121no—
354C3×C4—241no—
355C3×C4C4×D1211yescharacteristic
356C3×C4#87611yescharacteristic
357C3×C4C4×#6711yescharacteristic
358C3×C4#93011yescharacteristic
359C3×C4C3×C4×D411yescharacteristic
360C3×C4C3×C4×D411yescharacteristic
361C3×C4C3×#12111yescharacteristic
362C3×C4C3×#12611yescharacteristic
363Dic3—41no—
364Dic3—81no—
365C32#193211yescharacteristic, complemented, Sylow
366C23—61no—
367C23C3×#23511yescharacteristic
368Q8—61no—
369Q8—61no—
370D4—61no—
371D4—61no—
372D4—121no—
373D4—121no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—61no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4C2×C3×C4×D311yescharacteristic
382C2×C4C2×C3×D1211yescharacteristic
383C2×C4C3×#23511yescharacteristic
384C2×C4C3×#23511yescharacteristic
385C2×C4C3×#23511yescharacteristic
386C2×C4C2×C3×#6711yescharacteristic
387C8—22no—
388C8—22no—
389C8—62no—
390C8—121no—
391C2×C3—22no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—41no—
400C2×C3—41no—
401C2×C3—241no—
402C2×C3#494011yescharacteristic
403C2×C3C3×#38811yescharacteristic
404D3—81no—
405C22—41no—
406C22—121no—
407C22—241no—
408C22C3×#87211yescharacteristic
409C22C3×#87511yescharacteristic
410C22C3×#92911yescharacteristic
411C4—22no—
412C4—41no—
413C4—121no—
414C4—241no—
415C4C3×C4×D1211yescharacteristic
416C4C3×#87611yescharacteristic
417C4C3×C4×#6711yescharacteristic
418C4C3×#93011yescharacteristic
419C3—21no—
420C3#6987411yescharacteristic, direct product factor
421C3C3×#193211yescharacteristic, complemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—241no—
426C2C3×#494011yescharacteristic
subgroupG/H
centerC3×C4#930
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×M16C2
socleC2×C32#388
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×#1932
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×C4×M16

Complements

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

NH ≅ G/Ntype
1. C32×C4×M16C2semidirect
4. C3×#5124C2semidirect
6. C3×#4559C2semidirect
7. C3×#4523C2semidirect
9. #69874C3direct (N × H)
20. C3×#824C4semidirect
21. C3×#823C4semidirect
30. C3×C4×M16D3semidirect
31. C3×C4×M16C2×C3semidirect
34. #5124C2×C3semidirect
38. #4559C2×C3semidirect
39. #4523C2×C3semidirect
99. #824C3×C4semidirect
100. #823C3×C4semidirect
133. C4×M16C3×D3semidirect
365. C32#1932semidirect
420. C3#69874direct (N × H)
421. C3C3×#1932semidirect

Maximal subgroups

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

subgroupindex
C32×C4×M162
C3×#51392
C3×#51322
C3×#51242
C2×C3×#8052
C3×#45592
C3×#45232
C3×#19323
#698743