Finite Group Databasebeta

← C3×#70077 #11794607

Subgroups — C3×#70077 #11794607

Order 1152.

525 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#100C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4C3×#5125C211yesmaximal, characteristic, complemented
5C3×#5124C211yesmaximal, characteristic, complemented
6C3×#5124C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8C3×#2069—31nomaximal
9#70077C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#100—22no—
18C3×#833—22no—
19C3×#833—22no—
20C3×#822—22no—
21C3×#822—22no—
22C3×#819—22no—
23C3×#430—31no—
24C3×#430—31no—
25C3×#430—31no—
26C2×C3×#100—21no—
27C2×C3×#100—31no—
28C2×C3×#100—31no—
29C2×C3×#100D311yescharacteristic
30C2×C3×#100C2×C311yescharacteristic
31C2×#833C2×C311yescharacteristic
32C2×#833C2×C311yescharacteristic
33#5125C2×C311yescharacteristic, complemented
34#5124C2×C311yescharacteristic, complemented
35#5124C2×C311yescharacteristic, complemented
36C3×#338—31no—
37C3⋊#338C2×C311yescharacteristic, complemented
38C24×C32Q812yes—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C22×C32×C4C2311yescharacteristic
46C32×M16—21no—
47C32×M16—21no—
48C32×M16—21no—
49C32×M16D412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C3×#208—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208D412yes—
59C3×#208D412yes—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#2069—31noSylow
65C22×C3×D4—21no—
66C22×C3×D4C2×D311yescharacteristic
67C22×C3×D4C22×C311yescharacteristic
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C2×#208C22×C311yescharacteristic
79C2×#208C22×C311yescharacteristic
80C2×#208C22×C311yescharacteristic
81C2×#208C22×C311yescharacteristic
82C3×#108—62no—
83C3×#108—62no—
84C3×#108—62no—
85C3×#100—24no—
86C3×#100—22no—
87C3×#100—22no—
88C3×#100—62no—
89C3×#100—62no—
90#833—22no—
91#833—22no—
92#822—22no—
93#822—22no—
94#819—22no—
95C23×C32—22no—
96C23×C32—22no—
97C23×C32—22no—
98C23×C32—82no—
99C23×C32C2×Q811yescharacteristic
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C32×C8—22no—
111C32×C8—41no—
112C3×C3⋊C8—22no—
113C3×C3⋊C8—22no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#430—31no—
117#430—31no—
118#430—31no—
119C2×#100—31no—
120C2×#100—31no—
121C2×#100C3×D311yescharacteristic
122#338—31no—
123C24×C3—22no—
124C24×C3Dic612yes—
125C24×C3C3×Q812yes—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4—21no—
139C2×C3×D4—21no—
140C2×C3×D4—41no—
141C2×C3×D4—41no—
142C2×C3×D4—41no—
143C2×C3×D4—41no—
144C22×C3×C4—21no—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C23×C311yescharacteristic
147C3×M16—21no—
148C3×M16—21no—
149C3×M16—22no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16—21no—
154C3×M16—22no—
155C3×M16—32no—
156C3×M16—32no—
157C3×M16—41no—
158C3×M16—41no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16—61no—
163C3×M16—61no—
164C3×M16—61no—
165C3×M16#6712yes—
166C3×M16C3×D412yes—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—41no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177#208—21no—
178#208—21no—
179#208—21no—
180#208—21no—
181#208—21no—
182#208—21no—
183#208C3×D412yes—
184#208C3×D412yes—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—21no—
189C22×C32—41no—
190C22×C32—42no—
191C22×C32—82no—
192C22×C32—82no—
193C22×C32—82no—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32C22⋊Q811yescharacteristic
196C22×C32C22⋊Q811yescharacteristic
197C32×C4#12111yescharacteristic
198C32×C4#12111yescharacteristic
199C32×C4#12111yescharacteristic
200C32×C4#12611yescharacteristic
201C22×D4C2×C3×D311yescharacteristic
202C2×M16—31no—
203C2×M16—31no—
204C2×M16—31no—
205C2×M16—31no—
206C2×M16C2×C3×D311yescharacteristic
207C2×M16C2×C3×D311yescharacteristic
208#108—62no—
209#108—62no—
210#108—62no—
211#100—22no—
212#100—62no—
213#100—62no—
214C23×C3—24no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—21no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3—82no—
225C23×C3—82no—
226C23×C3—84no—
227C23×C3C2×Dic611yescharacteristic
228C23×C3C2×C3×Q811yescharacteristic
229C3×D4—42no—
230C3×D4—42no—
231C3×D4—42no—
232C3×D4—42no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4#23511yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4#23711yescharacteristic
251C2×C3×C4#23711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×C3×D411yescharacteristic
254C2×C3×C4C2×C3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×C3×C4C3×#4111yescharacteristic
257C2×C3×C4C3×#4111yescharacteristic
258C2×C3×C4C3×#4111yescharacteristic
259C3×C8—22no—
260C3×C8—22no—
261C3×C8—42no—
262C3×C8—42no—
263C3×C8—41no—
264C3×C8—41no—
265C3×C8—62no—
266C3×C8—62no—
267C3×C8—121no—
268C3×C8—121no—
269C3⋊C8—22no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—41no—
273C2×C32—21no—
274C2×C32—21no—
275C2×C32—21no—
276C2×C32—82no—
277C2×C32#39611yescharacteristic
278C24C3×Dic612yes—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C22×C4C22×C3×D311yescharacteristic
286M16—21no—
287M16—21no—
288M16—21no—
289M16—32no—
290M16—32no—
291M16—61no—
292M16—61no—
293M16—61no—
294M16—61no—
295M16—61no—
296M16—61no—
297M16C3×#6712yes—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—61no—
303C2×C8—61no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—41no—
308C22×C3—41no—
309C22×C3—42no—
310C22×C3—44no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—82no—
314C22×C3—82no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—82no—
318C22×C3—82no—
319C22×C3—84no—
320C22×C3—84no—
321C22×C3—84no—
322C22×C3#87811yescharacteristic
323C22×C3#87811yescharacteristic
324C22×C3#92411yescharacteristic
325C22×C3C3×C22⋊Q811yescharacteristic
326C22×C3C3×C22⋊Q811yescharacteristic
327C22×C3C3×C22⋊Q811yescharacteristic
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4#87911yescharacteristic
333C3×C4#88411yescharacteristic
334C3×C4#93811yescharacteristic
335C3×C4#93911yescharacteristic
336C3×C4C3×#12111yescharacteristic
337C3×C4C3×#12111yescharacteristic
338C3×C4C3×#12111yescharacteristic
339C3×C4C3×#12611yescharacteristic
340C32#206911yescharacteristic, complemented, Sylow
341C23—22no—
342C23—22no—
343C23—22no—
344C23—82no—
345C23C2×C3×Dic611yescharacteristic
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350C2×C4C3×#23511yescharacteristic
351C2×C4C3×D3×D411yescharacteristic
352C2×C4C3×D3×D411yescharacteristic
353C2×C4C3×#23711yescharacteristic
354C2×C4C3×#23711yescharacteristic
355C2×C4C2×C3×#6711yescharacteristic
356C8—22no—
357C8—41no—
358C8—62no—
359C8—62no—
360C8—121no—
361C8—121no—
362C2×C3—22no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—41no—
371C2×C3—41no—
372C2×C3—84no—
373C2×C3—82no—
374C2×C3—82no—
375C2×C3#494811yescharacteristic
376C2×C3C3×#39611yescharacteristic
377C22—41no—
378C22—42no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22C3×#87811yescharacteristic
383C22C3×#87811yescharacteristic
384C22C3×#92411yescharacteristic
385C4C3×#87911yescharacteristic
386C4C3×#88411yescharacteristic
387C4C3×#93811yescharacteristic
388C4C3×#93911yescharacteristic
389C3—21no—
390C3#7007711yescharacteristic, direct product factor
391C3C3×#206911yescharacteristic, complemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—82no—
396C2C3×#494811yescharacteristic
subgroupG/H
centerC2×C3#4948
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#100C2
socleC2×C32#396
prime radicalC22×C32×D4C22
hypercenterC2×C3×#100D3
hypocenterC3C3×#2069
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#100

Complements

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

NH ≅ G/Ntype
4. C3×#5125C2semidirect
5. C3×#5124C2semidirect
6. C3×#5124C2semidirect
7. C3×C3⋊#338C2semidirect
9. #70077C3direct (N × H)
33. #5125C2×C3semidirect
34. #5124C2×C3semidirect
35. #5124C2×C3semidirect
37. C3⋊#338C2×C3semidirect
340. C32#2069semidirect
390. C3#70077direct (N × H)
391. C3C3×#2069semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1002
C2×C3×#8332
C3×#51252
C3×#51242
C3×C3⋊#3382
C3×#20693
#700773