Finite Group Databasebeta

← C3×#68208 #11780097

Subgroups — C3×#68208 #11780097

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3C3×#4846C211yesmaximal, characteristic, complemented
4C3×#4682C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1647—31nomaximal
9#68208C311yesmaximal, characteristic, direct product factor
10C2×C3×#237—21no—
11C32×C4×D4C2211yescharacteristic
12C2×C3×#214—21no—
13C3×#930—21no—
14C2×C3×C4⋊Dic3—21no—
15C3×#897—21no—
16C3×#886—22no—
17C3×C4×D12C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22C3×#821—21no—
23C3×#818—22no—
24C3×#818—21no—
25C3×#810—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×#547—31no—
28#5555C2×C311yescharacteristic
29C3×#500—31no—
30C3×#474—31no—
31C3×#461—31no—
32#5019C2×C311yescharacteristic, complemented
33#4846C2×C311yescharacteristic, complemented
34#4682C2×C311yescharacteristic, complemented
35C3×#332—31no—
36C3×D4⋊C8—21no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8D311yescharacteristic, complemented
39C3×D4⋊C8C2×C311yescharacteristic, complemented
40#4486C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×C3×#67—22no—
45C22×C3×Dic3—22no—
46C3×#237—42no—
47C3×#237—42no—
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42C2311yescharacteristic
57C3×#214—42no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—22no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D412yes—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67#1647—31noSylow
68C2×C3×#41—61no—
69C2×#237—21no—
70C2×C3×SD16—61no—
71C3×C4⋊Q8—31no—
72C3×C4⋊Q8—31no—
73C3×#123—62no—
74C3×C22⋊Q8—61no—
75C3×#121—61no—
76C3×C4×D4—21no—
77C3×C4×D4—31no—
78C3×C4×D4C2×D311yescharacteristic
79C3×C4×D4C22×C311yescharacteristic
80C2×C3×C4⋊C4—61no—
81C2×#214—21no—
82#930—21no—
83C2×C4⋊Dic3—21no—
84#897—21no—
85#886—22no—
86C4×D12C22×C311yescharacteristic
87#869C22×C311yescharacteristic
88#869C22×C311yescharacteristic
89C3×#107—61no—
90C3×#107—62no—
91C3×C4⋊C8—21no—
92C3×C4⋊C8—31no—
93C3×C4⋊C8C2×D311yescharacteristic
94C3×C4⋊C8C22×C311yescharacteristic
95C3×#103—61no—
96C3×#102—61no—
97C3×C4×C8—21no—
98C3×C4×C8C2×D311yescharacteristic
99C3×C4×C8C22×C311yescharacteristic
100#821—21no—
101#818—22no—
102#818—21no—
103#810—21no—
104C4⋊(C3⋊C8)C22×C311yescharacteristic
105C23×C32—21no—
106C22×C3×D3—21no—
107C32×D4—21no—
108C32×D4D812yes—
109C2×C32×C4—21no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C3×#67—44no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—44no—
119C2×C3×Dic3—41no—
120C3×D12—21no—
121C3×D12—21no—
122C3×C4×D3—41no—
123C3×C4×D3—41no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6—41no—
128C32×C8—22no—
129C32×C8—41no—
130C3×C3⋊C8—41no—
131#547—31no—
132#500—31no—
133#474—31no—
134#461—31no—
135#332—31no—
136D4⋊C8—31no—
137D4⋊C8C3×D311yescharacteristic, complemented
138C3×#41—122no—
139C3×#41—122no—
140C2×C3×Q8—61no—
141C2×C3×Q8—61no—
142C2×C3×D4—21no—
143C2×C3×D4—31no—
144C2×C3×D4—62no—
145C2×C3×D4D1211yescharacteristic
146C2×C3×D4C3×D411yescharacteristic
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—41no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152C2×#67—22no—
153C22×Dic3—22no—
154#237—42no—
155#237—42no—
156C2×D12C3×D411yescharacteristic
157C2×C4×D3—21no—
158C2×Dic6—21no—
159C2×Dic6—21no—
160C3×SD16—122no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—21no—
165C2×C3×C8—41no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—32no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4D1211yescharacteristic
176C3×C4⋊C4C3×D411yescharacteristic
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—41no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—61no—
182C3×C42—21no—
183C3×C42C22×D311yescharacteristic
184C3×C42C23×C311yescharacteristic
185#214—42no—
186(C2×D3)⋊C4—22no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3—22no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3C3×D412yes—
193C4⋊Dic3C3×D411yescharacteristic
194C2×C3⋊C8—21no—
195C22×C32—22no—
196C22×C32—41no—
197C22×C32—41no—
198C22×C32#12011yescharacteristic
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C32×C4—21no—
203C32×C4—41no—
204C32×C4C2×D811yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—42no—
209C3×Dic3—41no—
210C3×Dic3—81no—
211C2×#41—61no—
212C2×SD16—61no—
213C4⋊Q8—31no—
214C4⋊Q8—31no—
215#123—62no—
216C22⋊Q8—61no—
217#121—61no—
218C4×D4—31no—
219C4×D4C2×C3×D311yescharacteristic
220C2×C4⋊C4—61no—
221#107—61no—
222#107—62no—
223C4⋊C8—31no—
224C4⋊C8C2×C3×D311yescharacteristic
225#103—61no—
226#102—61no—
227C4×C8C2×C3×D311yescharacteristic
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—41no—
231C23×C3—61no—
232C22×D3—21no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×Q8—121no—
236C3×Q8—121no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—22no—
240C3×D4—41no—
241C3×D4—61no—
242C3×D4—61no—
243C3×D4—124no—
244C3×D4D2412yes—
245C3×D4C3×D812yes—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—61no—
257C2×C3×C4—62no—
258C2×C3×C4—81no—
259C2×C3×C4—81no—
260C2×C3×C4—124no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×C3×D411yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269C2×C3×C4C2×C3×D411yescharacteristic
270#67—44no—
271C2×Dic3—22no—
272C2×Dic3—21no—
273C2×Dic3—44no—
274C2×Dic3—41no—
275D12—21no—
276D12—21no—
277C4×D3—41no—
278C4×D3—41no—
279Dic6—41no—
280Dic6—41no—
281Dic6—41no—
282Dic6—41no—
283C3×C8—22no—
284C3×C8—22no—
285C3×C8—42no—
286C3×C8—41no—
287C3×C8—41no—
288C3×C8—81no—
289C3×C8—121no—
290C3⋊C8—41no—
291C2×C32—42no—
292C2×C32#44711yescharacteristic
293C2×C32#45211yescharacteristic
294C2×C32#45611yescharacteristic
295C3×D3—81no—
296#41—122no—
297#41—122no—
298C2×Q8—61no—
299C2×Q8—61no—
300C2×D4—31no—
301C2×D4—62no—
302C2×D4C3×D1211yescharacteristic
303C22×C4—21no—
304C22×C4—62no—
305C22×C4—61no—
306SD16—122no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—61no—
310C4⋊C4—31no—
311C4⋊C4—32no—
312C4⋊C4—62no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4C3×D1211yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—62no—
319C22⋊C4—61no—
320C42C22×C3×D311yescharacteristic
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—21no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3—121no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3#88211yescharacteristic
335C22×C3C3×#12011yescharacteristic
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—81no—
349C3×C4—121no—
350C3×C4—122no—
351C3×C4—241no—
352C3×C4C2×D2411yescharacteristic
353C3×C4#90811yescharacteristic
354C3×C4#91211yescharacteristic
355C3×C4#91511yescharacteristic
356C3×C4C2×C3×D811yescharacteristic
357C3×C4C3×#13511yescharacteristic
358C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
359C3×C4C3×#13711yescharacteristic
360Dic3—42no—
361Dic3—41no—
362Dic3—81no—
363C32#164711yescharacteristic, complemented, Sylow
364C23—21no—
365C23—61no—
366Q8—121no—
367Q8—121no—
368Q8—121no—
369Q8—121no—
370D4—21no—
371D4—61no—
372D4—61no—
373D4—124no—
374D4C3×D2412yes—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—61no—
379C2×C4—62no—
380C2×C4—124no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4C2×C3×D1211yescharacteristic
385C2×C4C3×D3×D411yescharacteristic
386C2×C4C3×D3×D411yescharacteristic
387C8—22no—
388C8—41no—
389C8—121no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—42no—
394C2×C3—42no—
395C2×C3—82no—
396C2×C3—241no—
397C2×C3#473211yescharacteristic
398C2×C3#478311yescharacteristic
399C2×C3#482611yescharacteristic
400C2×C3C3×#44711yescharacteristic
401C2×C3C3×#45211yescharacteristic
402C2×C3C3×#45611yescharacteristic
403D3—81no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—121no—
408C22—121no—
409C22—121no—
410C22C3×#88211yescharacteristic
411C4—21no—
412C4—41no—
413C4—121no—
414C4—122no—
415C4—241no—
416C4C2×C3×D2411yescharacteristic
417C4C3×#90811yescharacteristic
418C4C3×#91211yescharacteristic
419C4C3×#91511yescharacteristic
420C3—21no—
421C3#6820811yescharacteristic, direct product factor
422C3C3×#164711yescharacteristic, complemented
423C2—42no—
424C2—241no—
425C2C3×#473211yescharacteristic
426C2C3×#478311yescharacteristic
427C2C3×#482611yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC3×#5555C2
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1647
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5019C2semidirect
3. C3×#4846C2semidirect
4. C3×#4682C2semidirect
5. C32×D4⋊C8C2semidirect
6. C3×#4486C2semidirect
7. C3×#4459C2semidirect
9. #68208C3direct (N × H)
32. #5019C2×C3semidirect
33. #4846C2×C3semidirect
34. #4682C2×C3semidirect
38. C3×D4⋊C8D3semidirect
39. C3×D4⋊C8C2×C3semidirect
40. #4486C2×C3semidirect
41. #4459C2×C3semidirect
137. D4⋊C8C3×D3semidirect
363. C32#1647semidirect
421. C3#68208direct (N × H)
422. C3C3×#1647semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×#50192
C3×#48462
C3×#46822
C32×D4⋊C82
C3×#44862
C3×#44592
C3×#16473
#682083