Finite Group Databasebeta

← C3×#70730 #11794604

Subgroups — C3×#70730 #11794604

Order 1152.

483 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#430C211yesmaximal, characteristic, complemented
2C2×C3×#823C211yesmaximal, characteristic
3C2×C3×#823C211yesmaximal, characteristic
4C2×C3×#823C211yesmaximal, characteristic
5C3×#5125C211yesmaximal, characteristic, complemented
6C3×#5124C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8C3×#2069—31nomaximal
9#70730C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C32×#108—22no—
18C3×#823—22no—
19C3×#823—22no—
20C3×#823—22no—
21C3×#822—22no—
22C3×#819—22no—
23C3×#430—21no—
24C3×#430—31no—
25C3×#430—31no—
26C3×#430D311yescharacteristic, complemented
27C3×#430C2×C311yescharacteristic, complemented
28C2×C3×#100—31no—
29C2×C3×#100—31no—
30C2×C3×#100—31no—
31C2×#823C2×C311yescharacteristic
32C2×#823C2×C311yescharacteristic
33C2×#823C2×C311yescharacteristic
34#5125C2×C311yescharacteristic, complemented
35#5124C2×C311yescharacteristic, complemented
36C3×#338—31no—
37C3⋊#338C2×C311yescharacteristic, complemented
38C23×C3×D3Q812yes—
39C22×C32×C4C2311yescharacteristic
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×M16—21no—
47C32×M16—21no—
48C32×M16—21no—
49C32×M16—21no—
50C32×M16D412yes—
51C32×M16D412yes—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208D412yes—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#2069—31noSylow
65C22×C3×D4—31no—
66C22×D12C22×C311yescharacteristic
67C2×C3×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16—31no—
71C2×C3×M16—31no—
72C2×C3×M16—31no—
73C2×C3×M16C2×D311yescharacteristic
74C2×C3×M16C2×D311yescharacteristic
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×M16C22×C311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C2×C3×M16C22×C311yescharacteristic
79C2×#208C22×C311yescharacteristic
80C2×#208C22×C311yescharacteristic
81C2×#208C22×C311yescharacteristic
82C3×#108—24no—
83C3×#108—22no—
84C3×#108—22no—
85C3×#108—62no—
86C3×#108—62no—
87C3×#100—62no—
88C3×#100—62no—
89C3×#100—62no—
90#823—22no—
91#823—22no—
92#823—22no—
93#822—22no—
94#819—22no—
95C23×C32C2×Q811yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—22no—
98C22×C3×D3—22no—
99C22×C3×D3—82no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C32×C8—22no—
111C32×C8—22no—
112C32×C8—41no—
113C3×C3⋊C8—22no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#430—31no—
117#430—31no—
118#430C3×D311yescharacteristic, complemented
119C2×#100—31no—
120C2×#100—31no—
121C2×#100—31no—
122#338—31no—
123C24×C3—32no—
124C23×D3C3×Q812yes—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C22×C3×C4—21no—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C23×C311yescharacteristic
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×D12—21no—
140C3×M16—22no—
141C3×M16—21no—
142C3×M16—21no—
143C3×M16—21no—
144C3×M16—21no—
145C3×M16—22no—
146C3×M16—21no—
147C3×M16—21no—
148C3×M16—21no—
149C3×M16—21no—
150C3×M16—22no—
151C3×M16—22no—
152C3×M16—32no—
153C3×M16—41no—
154C3×M16—41no—
155C3×M16—61no—
156C3×M16—61no—
157C3×M16—61no—
158C3×M16—61no—
159C3×M16—61no—
160C3×M16D1212yes—
161C3×M16#6712yes—
162C3×M16C3×D412yes—
163C3×M16C3×D412yes—
164C2×C3×C8—22no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
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—
176#208—21no—
177#208—21no—
178#208—21no—
179#208—21no—
180#208—21no—
181#208C3×D412yes—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C22×C32—41no—
186C22×C32C22⋊Q811yescharacteristic
187C22×C32C22⋊Q811yescharacteristic
188C22×C32C22⋊Q811yescharacteristic
189C2×C3×D3—42no—
190C2×C3×D3—82no—
191C2×C3×D3—82no—
192C2×C3×D3—82no—
193C32×C4#12111yescharacteristic
194C32×C4#12111yescharacteristic
195C32×C4#12111yescharacteristic
196C32×C4#12611yescharacteristic
197C22×D4—31no—
198C2×M16—31no—
199C2×M16—31no—
200C2×M16—31no—
201C2×M16C2×C3×D311yescharacteristic
202C2×M16C2×C3×D311yescharacteristic
203C2×M16C2×C3×D311yescharacteristic
204#108—22no—
205#108—62no—
206#108—62no—
207#100—62no—
208#100—62no—
209#100—62no—
210C23×C3—21no—
211C23×C3—62no—
212C23×C3—62no—
213C23×C3—62no—
214C23×C3—242no—
215C23×C3D3×Q811yescharacteristic
216C23×C3C2×C3×Q811yescharacteristic
217C22×D3—22no—
218C22×D3—22no—
219C22×D3—22no—
220C22×D3—82no—
221C3×D4—121no—
222C3×D4—121no—
223C3×D4—121no—
224C3×D4—121no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4C2×D1211yescharacteristic
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4#23911yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×C3×D411yescharacteristic
238C2×C3×C4C2×C3×D411yescharacteristic
239C2×C3×C4C2×C3×D411yescharacteristic
240C2×C3×C4C3×#4111yescharacteristic
241C2×C3×C4C3×#4111yescharacteristic
242C2×C3×C4C3×#4111yescharacteristic
243D12—41no—
244D12—41no—
245D12—41no—
246D12—41no—
247C3×C8—24no—
248C3×C8—22no—
249C3×C8—22no—
250C3×C8—22no—
251C3×C8—22no—
252C3×C8—42no—
253C3×C8—42no—
254C3×C8—41no—
255C3×C8—41no—
256C3×C8—62no—
257C3×C8—121no—
258C3×C8—121no—
259C3⋊C8—22no—
260C3⋊C8—41no—
261C3⋊C8—41no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32—21no—
265C2×C32#39611yescharacteristic
266C3×D3—82no—
267C24—32no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4—61no—
272C2×D4—61no—
273C2×D4—61no—
274C22×C4C22×C3×D311yescharacteristic
275M16—21no—
276M16—21no—
277M16—21no—
278M16—21no—
279M16—32no—
280M16—61no—
281M16—61no—
282M16—61no—
283M16—61no—
284M16—61no—
285M16C3×D1212yes—
286M16C3×#6712yes—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—61no—
291C2×C8—61no—
292C2×C8—61no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—81no—
299C22×C3—122no—
300C22×C3—242no—
301C22×C3—242no—
302C22×C3—242no—
303C22×C3#89611yescharacteristic
304C22×C3#89711yescharacteristic
305C22×C3#94611yescharacteristic
306C22×C3C3×C22⋊Q811yescharacteristic
307C22×C3C3×C22⋊Q811yescharacteristic
308C22×C3C3×C22⋊Q811yescharacteristic
309C2×D3—42no—
310C2×D3—82no—
311C2×D3—82no—
312C2×D3—82no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4#89511yescharacteristic
318C3×C4#89811yescharacteristic
319C3×C4#93011yescharacteristic
320C3×C4#93911yescharacteristic
321C3×C4C3×#12111yescharacteristic
322C3×C4C3×#12111yescharacteristic
323C3×C4C3×#12111yescharacteristic
324C3×C4C3×#12611yescharacteristic
325C32#206911yescharacteristic, complemented, Sylow
326C23—62no—
327C23—62no—
328C23—62no—
329C23—242no—
330C23C3×D3×Q811yescharacteristic
331D4—121no—
332D4—121no—
333D4—121no—
334D4—121no—
335C2×C4C2×C3×D1211yescharacteristic
336C2×C4C3×#23511yescharacteristic
337C2×C4C3×D3×D411yescharacteristic
338C2×C4C3×#23711yescharacteristic
339C2×C4C3×#23911yescharacteristic
340C2×C4C2×C3×#6711yescharacteristic
341C8—22no—
342C8—22no—
343C8—41no—
344C8—62no—
345C8—121no—
346C8—121no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—41no—
355C2×C3—41no—
356C2×C3—41no—
357C2×C3—242no—
358C2×C3#499411yescharacteristic
359C2×C3C3×#39611yescharacteristic
360D3—82no—
361C22—41no—
362C22—122no—
363C22—242no—
364C22—242no—
365C22—242no—
366C22C3×#89611yescharacteristic
367C22C3×#89711yescharacteristic
368C22C3×#94611yescharacteristic
369C4C3×#89511yescharacteristic
370C4C3×#89811yescharacteristic
371C4C3×#93011yescharacteristic
372C4C3×#93911yescharacteristic
373C3—21no—
374C3#7073011yescharacteristic, direct product factor
375C3C3×#206911yescharacteristic, complemented
376C2—21no—
377C2—21no—
378C2—21no—
379C2—242no—
380C2C3×#499411yescharacteristic
subgroupG/H
centerC2×C3#4994
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#430C2
socleC2×C32#396
prime radicalC22×C3×D12C22
hypercenterC3×#430D3
hypocenterC3C3×#2069
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#430

Complements

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

NH ≅ G/Ntype
1. C32×#430C2semidirect
5. C3×#5125C2semidirect
6. C3×#5124C2semidirect
7. C3×C3⋊#338C2semidirect
9. #70730C3direct (N × H)
26. C3×#430D3semidirect
27. C3×#430C2×C3semidirect
34. #5125C2×C3semidirect
35. #5124C2×C3semidirect
37. C3⋊#338C2×C3semidirect
118. #430C3×D3semidirect
325. C32#2069semidirect
374. C3#70730direct (N × H)
375. C3C3×#2069semidirect

Maximal subgroups

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

subgroupindex
C32×#4302
C2×C3×#8232
C3×#51252
C3×#51242
C3×C3⋊#3382
C3×#20693
#707303