Finite Group Databasebeta

← C3×#70058 #11796290

Subgroups — C3×#70058 #11796290

Order 1152.

547 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic
2C32×#410C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4C3×#4472C214yesmaximal, complemented
5C3×#2123—31nomaximal
6#70058C311yesmaximal, characteristic, direct product factor
7C2×C32×#41C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C32×#117—21no—
10C3×#944—21no—
11C3×#936—21no—
12C3×#935C412yescomplemented
13C3×#935C2212yes—
14C3×#926C411yescharacteristic, complemented
15C3×#924—21no—
16C3×#924—21no—
17C2×C3×#208—21no—
18C32×#99—21no—
19C32×#99C2212yes—
20C3×#836—21no—
21C3×#833C2212yes—
22C3×#536—31no—
23#5825C2×C311yescharacteristic
24C3×#413—31no—
25C3×#410—21no—
26C3×#410D311yescharacteristic
27C3×#410C2×C311yescharacteristic
28#5237C2×C311yescharacteristic
29C3×#352—34no—
30#4472C2×C314yescomplemented
31C32×#41—41no—
32C32×#41—41no—
33C2×C32×Q8D411yescharacteristic
34C2×C32×D4C2×C411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4C2311yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C3×Dic3C2×C412yes—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—41no—
44C2×C3×Dic6—41no—
45C32×C4⋊C4—41no—
46C32×C22⋊C4—22no—
47C32×C42—41no—
48C3×#217—22no—
49C3×#217—22no—
50C3×#217C2×C412yes—
51C3×C4⋊Dic3—21no—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—22no—
54C3×C4×Dic3—21no—
55C3×#208—22no—
56C3×#208—41no—
57C2×C3×C3⋊C8—41no—
58#2123—31noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C22×C311yescharacteristic
62C22×C3×Q8—31no—
63C22×Dic6C3×C411yescharacteristic, complemented
64C2×C3×M16—61no—
65C3×C4⋊Q8—61no—
66C3×#124—61no—
67C3×#123—32no—
68C3×#123—32no—
69C3×C22⋊Q8—61no—
70C3×C22⋊Q8—61no—
71C3×#117—22no—
72C3×#117—21no—
73C3×#117—21no—
74C3×#117—31no—
75#944—21no—
76#936—21no—
77#935C3×C412yescomplemented
78#935C22×C312yes—
79#926C3×C411yescharacteristic, complemented
80#924—21no—
81#924—21no—
82C2×#208—21no—
83C3×#101—61no—
84C3×#100—32no—
85C3×#99—22no—
86C3×#99—21no—
87C3×#99—21no—
88C3×#99—22no—
89C3×#99C2×D312yes—
90C3×#99C22×C312yes—
91#836—21no—
92#833C22×C312yes—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22×C411yescharacteristic
95C23×C32C2×D411yescharacteristic
96C32×Q8—41no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—42no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—42no—
114C3×Dic6—42no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C3×C3⋊C8—42no—
118#536—31no—
119#413—31no—
120#410C3×D311yescharacteristic
121#352—34no—
122C3×#41—41no—
123C3×#41—41no—
124C3×#41—41no—
125C3×#41—41no—
126C3×#41—42no—
127C3×#41—42no—
128C2×C3×Q8—21no—
129C2×C3×Q8—61no—
130C2×C3×Q8—61no—
131C2×C3×Q8—121no—
132C2×C3×Q8—121no—
133C2×C3×Q8D1211yescharacteristic
134C2×C3×Q8C3×D411yescharacteristic
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—21no—
138C2×C3×D4C4×D311yescharacteristic
139C2×C3×D4#6711yescharacteristic
140C2×C3×D4C2×C3×C411yescharacteristic
141C2×C3×D4C3×D411yescharacteristic
142C2×C3×D4C22×D311yescharacteristic
143C2×C3×D4C23×C311yescharacteristic
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—32no—
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4C2×C3×C411yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C22×C3×C4C3×D411yescharacteristic
154C22×Dic3C2×C3×C412yes—
155C2×Dic6—21no—
156C2×Dic6—21no—
157C2×Dic6—41no—
158C2×Dic6—41no—
159C3×M16—62no—
160C3×M16—121no—
161C2×C3×C8—121no—
162C3×C4⋊C4—42no—
163C3×C4⋊C4—41no—
164C3×C4⋊C4—41no—
165C3×C4⋊C4—62no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—62no—
168C3×C22⋊C4—24no—
169C3×C22⋊C4—22no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—32no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—62no—
174C3×C42—42no—
175C3×C42—41no—
176C3×C42—41no—
177C3×C42—61no—
178#217—22no—
179#217—22no—
180#217C2×C3×C412yes—
181C4⋊Dic3—21no—
182Dic3⋊C4—22no—
183Dic3⋊C4—22no—
184C4×Dic3—21no—
185#208—22no—
186#208—41no—
187C2×C3⋊C8—41no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32C2×C22⋊C411yescharacteristic
195C32×C4—21no—
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—82no—
199C32×C4#9911yescharacteristic
200C32×C4#9911yescharacteristic
201C3×Dic3—42no—
202C3×Dic3—42no—
203C2×#41C2×C3×D311yescharacteristic
204C22×Q8—31no—
205C2×M16—61no—
206C4⋊Q8—61no—
207#124—61no—
208#123—32no—
209#123—32no—
210C22⋊Q8—61no—
211C22⋊Q8—61no—
212#117—21no—
213#117—31no—
214#101—61no—
215#100—32no—
216#99—21no—
217#99C2×C3×D312yes—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—21no—
221C23×C3(C2×D3)⋊C411yescharacteristic
222C23×C3C3×C22⋊C411yescharacteristic
223C23×C3C2×C4×D311yescharacteristic
224C23×C3C2×#6711yescharacteristic
225C23×C3C22×C3×C411yescharacteristic
226C23×C3C2×C3×D411yescharacteristic
227C3×Q8—41no—
228C3×Q8—41no—
229C3×Q8—42no—
230C3×Q8—122no—
231C3×Q8—121no—
232C3×Q8—121no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
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—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—44no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—62no—
268C2×C3×C4—62no—
269C2×C3×C4—122no—
270C2×C3×C4(C2×D3)⋊C411yescharacteristic
271C2×C3×C4(C2×D3)⋊C411yescharacteristic
272C2×C3×C4(C2×D3)⋊C411yescharacteristic
273C2×C3×C4C3×C22⋊C411yescharacteristic
274C2×C3×C4C3×C22⋊C411yescharacteristic
275C2×C3×C4C3×C22⋊C411yescharacteristic
276C2×C3×C4C2×D1211yescharacteristic
277C2×C3×C4C2×C3×D411yescharacteristic
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—42no—
281Dic6—42no—
282Dic6—41no—
283Dic6—41no—
284C3×C8—122no—
285C3⋊C8—42no—
286C2×C32—21no—
287C2×C32—41no—
288C2×C32—41no—
289C2×C32—41no—
290C2×C32C2×#9911yescharacteristic
291#41—41no—
292#41—41no—
293C2×Q8—61no—
294C2×Q8—61no—
295C2×Q8—121no—
296C2×Q8—121no—
297C2×Q8C3×D1211yescharacteristic
298C2×D4C3×C4×D311yescharacteristic
299C2×D4C3×#6711yescharacteristic
300C2×D4C22×C3×D311yescharacteristic
301C22×C4—32no—
302C22×C4C3×C4×D311yescharacteristic
303C22×C4C3×D1211yescharacteristic
304C22×C4C3×#6711yescharacteristic
305M16—62no—
306M16—121no—
307C2×C8—121no—
308C4⋊C4—41no—
309C4⋊C4—61no—
310C4⋊C4—62no—
311C4⋊C4—62no—
312C22⋊C4—22no—
313C22⋊C4—32no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C42—41no—
317C42—61no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3C2×(C2×D3)⋊C411yescharacteristic
338C22×C3C2×C3×C22⋊C411yescharacteristic
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—84no—
351C3×C4—82no—
352C3×C4—82no—
353C3×C4—122no—
354C3×C4—122no—
355C3×C4#80611yescharacteristic
356C3×C4#80611yescharacteristic
357C3×C4C3×#9911yescharacteristic
358C3×C4C3×#9911yescharacteristic
359Dic3—42no—
360Dic3—42no—
361C32#212311yescharacteristic, complemented, Sylow
362C23C3×(C2×D3)⋊C411yescharacteristic
363C23C2×C3×C4×D311yescharacteristic
364C23C2×C3×#6711yescharacteristic
365Q8—41no—
366Q8—122no—
367Q8—121no—
368Q8—121no—
369D4—41no—
370D4—41no—
371D4—41no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—42no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—122no—
382C2×C4C3×(C2×D3)⋊C411yescharacteristic
383C2×C4C3×(C2×D3)⋊C411yescharacteristic
384C2×C4C3×(C2×D3)⋊C411yescharacteristic
385C2×C4C2×C3×D1211yescharacteristic
386C8—122no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—41no—
391C2×C3—42no—
392C2×C3—41no—
393C2×C3—41no—
394C2×C3—41no—
395C2×C3—41no—
396C2×C3—41no—
397C2×C3—41no—
398C2×C3—81no—
399C2×C3—81no—
400C2×C3C2×#80611yescharacteristic
401C2×C3C2×C3×#9911yescharacteristic
402C22—21no—
403C22—21no—
404C22—21no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C2×C3×(C2×D3)⋊C411yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—82no—
413C4—122no—
414C4—122no—
415C4C3×#80611yescharacteristic
416C4C3×#80611yescharacteristic
417C3—21no—
418C3#7005811yescharacteristic, direct product factor
419C3C3×#212311yescharacteristic, complemented
420C2—21no—
421C2—41no—
422C2—41no—
423C2—41no—
424C2C2×C3×#80611yescharacteristic
subgroupG/H
centerC2×C3C2×#806
commutatorC23×C3C22×C3×C4
FrattiniC2×D4C22×C3×D3
FittingC32×#410C2
socleC2×C32C2×#99
prime radicalC2×C32×#41C22
cosocleC2×C3×D4C23×C3
hypercenterC3×#410D3
hypocenterC3C3×#2123
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#410

Complements

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

NH ≅ G/Ntype
4. C3×#4472C2semidirect
6. #70058C3direct (N × H)
8. C22×C3×Dic6C4semidirect
12. C3×#935C4semidirect
14. C3×#926C4semidirect
30. #4472C2×C3semidirect
63. C22×Dic6C3×C4semidirect
77. #935C3×C4semidirect
79. #926C3×C4semidirect
361. C32#2123semidirect
418. C3#70058direct (N × H)
419. C3C3×#2123semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C32×#4102
C3×#52372
C3×#44722
C3×#21233
#700583