Finite Group Databasebeta

← C3×#70322 #11794992

Subgroups — C3×#70322 #11794992

Order 1152.

503 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#418C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C3×#5215C211yesmaximal, characteristic
4C3×#5124C211yesmaximal, characteristic, complemented
5C3×#4559C211yesmaximal, characteristic, complemented
6C3×#4533C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8C3×#2081—31nomaximal
9#70322C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#102—22no—
18C3×#833—22no—
19C3×#832—22no—
20C3×#822—22no—
21C3×#430—31no—
22C3×#418—21no—
23C3×#418—31no—
24C3×#418D311yescharacteristic
25C3×#418C2×C311yescharacteristic
26C2×C3×#100—31no—
27C2×#833C2×C311yescharacteristic
28#5215C2×C311yescharacteristic
29#5124C2×C311yescharacteristic, complemented
30C3×#344—31no—
31C3×#344—31no—
32C3×H(3,ℤ/4)—31no—
33#4559C2×C311yescharacteristic, complemented
34#4533C2×C311yescharacteristic, complemented
35#4531C2×C311yescharacteristic, complemented
36C24×C32—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4D412yes—
43C22×C32×C4C2311yescharacteristic
44C32×M16—21no—
45C32×M16—21no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C22⋊C4—21no—
49C32×C42—21no—
50C3×#217—21no—
51C3×C4⋊Dic3—21no—
52C3×C4×Dic3—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8D412yes—
62#2081—31noSylow
63C22×C3×D4—21no—
64C22×C3×D4C2×D311yescharacteristic
65C22×C3×D4C22×C311yescharacteristic
66C2×C3×M16—21no—
67C2×C3×M16—31no—
68C2×C3×M16—31no—
69C2×C3×M16—31no—
70C2×C3×M16C2×D311yescharacteristic
71C2×C3×M16C22×C311yescharacteristic
72C3×#117—21no—
73C3×#117—31no—
74C3×#117C2×D311yescharacteristic
75C3×#117C22×C311yescharacteristic
76#926C22×C311yescharacteristic
77C2×#208C22×C311yescharacteristic
78C2×#208C22×C311yescharacteristic
79C2×#208C22×C311yescharacteristic
80C3×#108—62no—
81C3×#102—24no—
82C3×#102—22no—
83C3×#102—22no—
84C3×#102—62no—
85C3×#100—62no—
86#833—22no—
87#832—22no—
88#822—22no—
89C23×C32—22no—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32—82no—
93C23×C32#4111yescharacteristic
94C32×D4—22no—
95C32×D4—22no—
96C32×D4—41no—
97C32×D4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—41no—
106C32×C8—41no—
107C3×C3⋊C8—22no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#430—31no—
111#418—31no—
112#418C3×D311yescharacteristic
113C2×#100—31no—
114#344—31no—
115#344—31no—
116H(3,ℤ/4)—31no—
117C24×C3—21no—
118C24×C3—21no—
119C24×C3—41no—
120C2×C3×D4—22no—
121C2×C3×D4—22no—
122C2×C3×D4—21no—
123C2×C3×D4—21no—
124C2×C3×D4—21no—
125C2×C3×D4—21no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—22no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C2×C3×D4—41no—
136C2×C3×D4#6712yes—
137C2×C3×D4C3×D412yes—
138C22×C3×C4—21no—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C23×C311yescharacteristic
141C3×M16—21no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16—41no—
146C3×M16—41no—
147C3×M16—61no—
148C3×M16—61no—
149C3×M16—61no—
150C3×M16—61no—
151C3×M16—61no—
152C3×M16—61no—
153C2×C3×C8—22no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—32no—
157C2×C3×C8—61no—
158C2×C3×C8—61no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—61no—
163C3×C22⋊C4—21no—
164C3×C22⋊C4—21no—
165C3×C22⋊C4—41no—
166C3×C22⋊C4—61no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—41no—
170C3×C42—61no—
171#217—21no—
172C4⋊Dic3—21no—
173C4×Dic3—21no—
174#208—21no—
175#208—21no—
176#208—21no—
177#208—21no—
178#208—21no—
179#208—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C2×C3⋊C8C3×D412yes—
183C22×C32—41no—
184C22×C32—42no—
185C22×C32—82no—
186C22×C32—82no—
187C22×C32—82no—
188C22×C32#12311yescharacteristic
189C22×C32#12411yescharacteristic
190C22×C32#12611yescharacteristic
191C32×C4—81no—
192C32×C4#12111yescharacteristic
193C32×C4#12311yescharacteristic
194C32×C4#12311yescharacteristic
195C32×C4#12611yescharacteristic
196C3×Dic3—81no—
197C22×D4C2×C3×D311yescharacteristic
198C2×M16—31no—
199C2×M16—31no—
200C2×M16—31no—
201C2×M16C2×C3×D311yescharacteristic
202#117—31no—
203#117C2×C3×D311yescharacteristic
204#108—62no—
205#102—22no—
206#102—62no—
207#100—62no—
208C23×C3—22no—
209C23×C3—22no—
210C23×C3—21no—
211C23×C3—42no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—82no—
219C23×C3—82no—
220C23×C3—84no—
221C23×C3#23711yescharacteristic
222C23×C3C3×#4111yescharacteristic
223C3×D4—24no—
224C3×D4—22no—
225C3×D4—22no—
226C3×D4—22no—
227C3×D4—22no—
228C3×D4—42no—
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—41no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—41no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—42no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—121no—
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4#23511yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4#23711yescharacteristic
249C2×C3×C4#23711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C2×C3×D411yescharacteristic
252C2×C3×C4C2×C3×D411yescharacteristic
253C2×C3×C4C3×#4111yescharacteristic
254C2×C3×C4C3×#4111yescharacteristic
255C2×C3×C4C3×#4111yescharacteristic
256C2×C3×C4C3×#4111yescharacteristic
257C2×Dic3—41no—
258C3×C8—42no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—62no—
262C3×C8—121no—
263C3×C8—121no—
264C3⋊C8—22no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C2×C32—21no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32—82no—
271C2×C32#39711yescharacteristic
272C24—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4C3×#6712yes—
279C22×C4C22×C3×D311yescharacteristic
280M16—21no—
281M16—21no—
282M16—61no—
283M16—61no—
284M16—61no—
285M16—61no—
286M16—61no—
287M16—61no—
288C2×C8—21no—
289C2×C8—32no—
290C2×C8—61no—
291C2×C8—61no—
292C4⋊C4—21no—
293C4⋊C4—61no—
294C22⋊C4—21no—
295C22⋊C4—61no—
296C42—21no—
297C42—61no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—42no—
304C22×C3—44no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—82no—
308C22×C3—82no—
309C22×C3—84no—
310C22×C3—82no—
311C22×C3—82no—
312C22×C3—82no—
313C22×C3—82no—
314C22×C3—84no—
315C22×C3—84no—
316C22×C3#87911yescharacteristic
317C22×C3#88511yescharacteristic
318C22×C3#93511yescharacteristic
319C22×C3C3×#12311yescharacteristic
320C22×C3C3×#12411yescharacteristic
321C22×C3C3×#12611yescharacteristic
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—82no—
327C3×C4—81no—
328C3×C4—81no—
329C3×C4—241no—
330C3×C4#87911yescharacteristic
331C3×C4#88311yescharacteristic
332C3×C4#92911yescharacteristic
333C3×C4#93911yescharacteristic
334C3×C4C3×#12111yescharacteristic
335C3×C4C3×#12311yescharacteristic
336C3×C4C3×#12311yescharacteristic
337C3×C4C3×#12611yescharacteristic
338Dic3—81no—
339C32#208111yescharacteristic, complemented, Sylow
340C23—22no—
341C23—41no—
342C23—41no—
343C23—82no—
344C23C3×#23711yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—41no—
350C2×C4—121no—
351C2×C4C3×#23511yescharacteristic
352C2×C4C3×#23511yescharacteristic
353C2×C4C3×D3×D411yescharacteristic
354C2×C4C3×#23711yescharacteristic
355C2×C4C3×#23711yescharacteristic
356C2×C4C2×C3×#6711yescharacteristic
357C8—41no—
358C8—62no—
359C8—121no—
360C8—121no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—41no—
370C2×C3—41no—
371C2×C3—84no—
372C2×C3—82no—
373C2×C3—82no—
374C2×C3#495211yescharacteristic
375C2×C3C3×#39711yescharacteristic
376C22—41no—
377C22—42no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22C3×#87911yescharacteristic
382C22C3×#88511yescharacteristic
383C22C3×#93511yescharacteristic
384C4—81no—
385C4—241no—
386C4C3×#87911yescharacteristic
387C4C3×#88311yescharacteristic
388C4C3×#92911yescharacteristic
389C4C3×#93911yescharacteristic
390C3—21no—
391C3#7032211yescharacteristic, direct product factor
392C3C3×#208111yescharacteristic, complemented
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2C3×#495211yescharacteristic
subgroupG/H
centerC2×C3#4952
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#418C2
socleC2×C32#397
prime radicalC22×C32×D4C22
hypercenterC3×#418D3
hypocenterC3C3×#2081
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
4. C3×#5124C2semidirect
5. C3×#4559C2semidirect
6. C3×#4533C2semidirect
7. C3×#4531C2semidirect
9. #70322C3direct (N × H)
29. #5124C2×C3semidirect
33. #4559C2×C3semidirect
34. #4533C2×C3semidirect
35. #4531C2×C3semidirect
339. C32#2081semidirect
391. C3#70322direct (N × H)
392. C3C3×#2081semidirect

Maximal subgroups

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

subgroupindex
C32×#4182
C2×C3×#8332
C3×#52152
C3×#51242
C3×#45592
C3×#45332
C3×#45312
C3×#20813
#703223