Finite Group Databasebeta

← C3×#69141 #11798715

Subgroups — C3×#69141 #11798715

Order 1152.

486 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5651C211yesmaximal, characteristic, complemented
2C3×#5053C211yesmaximal, characteristic
3C3×#4746C211yesmaximal, characteristic
4C3×#4742C211yesmaximal, characteristic
5C32×#352C211yesmaximal, characteristic, complemented
6C3×#4476C211yesmaximal, characteristic, complemented
7C3×#4473C211yesmaximal, characteristic, complemented
8C3×#2201—31nomaximal
9#69141C311yesmaximal, characteristic, direct product factor
10C3×#1004C2211yescharacteristic
11C32×#123C2211yescharacteristic
12C3×#936C2211yescharacteristic
13C3×#935C2211yescharacteristic
14C3×#929—21no—
15C3×#924—21no—
16C3×#909—21no—
17C3×#889—21no—
18C3×#888—21no—
19C3×#886—21no—
20C3×#879—21no—
21C3×#879—21no—
22C3×#878—21no—
23C32×#100C2211yescharacteristic
24C32×#99C2211yescharacteristic
25C3×#834C2211yescharacteristic
26C3×#825—21no—
27C3×#806—21no—
28C3×#806—21no—
29C3×#563—31no—
30#5651C2×C311yescharacteristic, complemented
31C3×#458—31no—
32C3×#458—31no—
33C3×#455—31no—
34#5053C2×C311yescharacteristic
35#4746C2×C311yescharacteristic
36#4742C2×C311yescharacteristic
37C3×#354—31no—
38C3×#352—21no—
39C3×#352—31no—
40C3×#352D311yescharacteristic, complemented
41C3×#352C2×C311yescharacteristic, complemented
42#4476C2×C311yescharacteristic, complemented
43#4473C2×C311yescharacteristic, complemented
44C2×C32×D4C2311yescharacteristic
45C22×C32×C4D411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3D411yescharacteristic
49C3×#237—41no—
50C3×D3×D4—41no—
51C3×#235—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×M16—21no—
55C32×C4⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C22⋊C4D411yescharacteristic
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217D411yescharacteristic
64C3×(C2×D3)⋊C4—41no—
65C3×(C2×D3)⋊C4—41no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—41no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C3×Dic3⋊C4—21no—
74C3×Dic3⋊C4—41no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3D411yescharacteristic
77C3×Dic12—41no—
78C3×#204—41no—
79#2201—31noSylow
80C3×H(5,𝔽2)—31no—
81#1004C22×C311yescharacteristic
82C3×#137—61no—
83C3×C4⋊Q8—61no—
84C3×#126—61no—
85C3×#126—61no—
86C3×#125—61no—
87C3×#124—31no—
88C3×#123—21no—
89C3×#123—31no—
90C3×#123—61no—
91C3×#123—61no—
92C3×#123C2×D311yescharacteristic
93C3×#123C22×C311yescharacteristic
94C3×C22⋊Q8—61no—
95C3×C22⋊Q8—61no—
96#936C22×C311yescharacteristic
97#935C22×C311yescharacteristic
98#929—21no—
99#924—21no—
100#909—21no—
101#889—21no—
102#888—21no—
103#886—21no—
104#879—21no—
105#879—21no—
106#878—21no—
107C3×#104—61no—
108C3×#100—21no—
109C3×#100C2×D311yescharacteristic
110C3×#100C22×C311yescharacteristic
111C3×#99—21no—
112C3×#99—31no—
113C3×#99—61no—
114C3×#99—61no—
115C3×#99C2×D311yescharacteristic
116C3×#99C22×C311yescharacteristic
117#834C22×C311yescharacteristic
118#825—21no—
119#806—21no—
120#806—21no—
121C23×C32C2×D411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C32×D4—41no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C3×#67—41no—
132C3×#67—41no—
133C3×#67—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—21no—
143C3×C4×D3—41no—
144C3×Dic6—21no—
145C3×Dic6—41no—
146C3×Dic6—81no—
147C32×C8—41no—
148#563—31no—
149#458—31no—
150#458—31no—
151#455—31no—
152#354—31no—
153#352—31no—
154#352C3×D311yescharacteristic, complemented
155C3×#41—61no—
156C3×#41—121no—
157C2×C3×Q8—31no—
158C2×C3×Q8—61no—
159C2×C3×D4—21no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—121no—
163C2×C3×D4C22×D311yescharacteristic
164C2×C3×D4C23×C311yescharacteristic
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4D1211yescharacteristic
168C22×C3×C4C3×D411yescharacteristic
169C2×#67—21no—
170C2×#67—21no—
171C22×Dic3C3×D411yescharacteristic
172#237—41no—
173D3×D4—41no—
174#235—21no—
175C2×Dic6—21no—
176C2×Dic6C3×D411yescharacteristic
177C3×Q16—121no—
178C3×SD16—121no—
179C3×M16—21no—
180C3×M16—21no—
181C3×M16—41no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—121no—
193C3×C4⋊C4—121no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—31no—
200C3×C22⋊C4—41no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—121no—
207C3×C22⋊C4—121no—
208C3×C22⋊C4D1211yescharacteristic
209C3×C22⋊C4C3×D411yescharacteristic
210C3×C42—31no—
211C3×C42—61no—
212#217—21no—
213#217—21no—
214#217—21no—
215#217—21no—
216#217C3×D411yescharacteristic
217(C2×D3)⋊C4—41no—
218(C2×D3)⋊C4—41no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—41no—
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225Dic3⋊C4—21no—
226Dic3⋊C4—21no—
227Dic3⋊C4—41no—
228C4×Dic3—21no—
229C4×Dic3C3×D411yescharacteristic
230Dic12—41no—
231#204—41no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32#12011yescharacteristic
237C2×C3×D3—41no—
238C2×C3×D3—81no—
239C2×C3×D3—81no—
240C32×C4—21no—
241C32×C4—41no—
242C32×C4—41no—
243C32×C4—81no—
244C3×Dic3—41no—
245C3×Dic3—41no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250H(5,𝔽2)—31no—
251#137—61no—
252C4⋊Q8—61no—
253#126—61no—
254#126—61no—
255#125—61no—
256#124—31no—
257#123—31no—
258#123—61no—
259#123—61no—
260#123C2×C3×D311yescharacteristic
261C22⋊Q8—61no—
262C22⋊Q8—61no—
263#104—61no—
264#100C2×C3×D311yescharacteristic
265#99—31no—
266#99—61no—
267#99—61no—
268#99C2×C3×D311yescharacteristic
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3C2×D1211yescharacteristic
274C23×C3D3×D411yescharacteristic
275C23×C3C2×C3×D411yescharacteristic
276C23×C3C2×C3×D411yescharacteristic
277C22×D3—21no—
278C22×D3—21no—
279C3×Q8—61no—
280C3×Q8—121no—
281C3×Q8—241no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—61no—
285C3×D4—81no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—81no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4C2×C3×D411yescharacteristic
313#67—41no—
314#67—41no—
315#67—41no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—21no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324D12—21no—
325C4×D3—41no—
326Dic6—21no—
327Dic6—41no—
328Dic6—81no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—81no—
332C2×C32—21no—
333C2×C32—41no—
334C2×C32—41no—
335C2×C32B(4,𝔽2)11yescharacteristic
336C3×D3—81no—
337#41—61no—
338#41—121no—
339C2×Q8—31no—
340C2×Q8—61no—
341C2×D4—61no—
342C2×D4—61no—
343C2×D4—121no—
344C2×D4C22×C3×D311yescharacteristic
345C22×C4—31no—
346C22×C4C3×D1211yescharacteristic
347Q16—121no—
348SD16—121no—
349M16—21no—
350C4⋊C4—21no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—61no—
358C4⋊C4—121no—
359C4⋊C4—121no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—31no—
363C22⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—121no—
368C22⋊C4—121no—
369C22⋊C4C3×D1211yescharacteristic
370C42—31no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—81no—
384C22×C3—81no—
385C22×C3—121no—
386C22×C3—241no—
387C22×C3—241no—
388C22×C3#88211yescharacteristic
389C22×C3C3×#12011yescharacteristic
390C2×D3—41no—
391C2×D3—81no—
392C2×D3—81no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—41no—
400C3×C4—81no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—81no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—121no—
407C3×C4—121no—
408C3×C4—121no—
409C3×C4—161no—
410C3×C4—241no—
411Dic3—41no—
412Dic3—41no—
413Dic3—41no—
414Dic3—41no—
415Dic3—41no—
416Dic3—81no—
417C32#220111yescharacteristic, complemented, Sylow
418C23—61no—
419C23—61no—
420C23C2×C3×D1211yescharacteristic
421C23C3×D3×D411yescharacteristic
422Q8—61no—
423Q8—121no—
424Q8—241no—
425D4—41no—
426D4—61no—
427D4—121no—
428D4—121no—
429D4—121no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4C3×D3×D411yescharacteristic
444C8—41no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—81no—
454C2×C3—81no—
455C2×C3—241no—
456C2×C3#474111yescharacteristic
457C2×C3C3×B(4,𝔽2)11yescharacteristic
458D3—81no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—121no—
464C22—241no—
465C22—241no—
466C22C3×#88211yescharacteristic
467C4—21no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—121no—
472C4—121no—
473C4—121no—
474C4—121no—
475C4—121no—
476C4—241no—
477C3—21no—
478C3#6914111yescharacteristic, direct product factor
479C3C3×#220111yescharacteristic, complemented
480C2—21no—
481C2—41no—
482C2—41no—
483C2—241no—
484C2C3×#474111yescharacteristic
subgroupG/H
centerC2×C3#4741
commutator, cosocleC2×C3×D4C23×C3
FrattiniC2×D4C22×C3×D3
FittingC32×#352C2
socleC2×C32B(4,𝔽2)
prime radicalC3×#1004C22
hypercenterC3×#352D3
hypocenterC3C3×#2201
LCSG ▷ C2×C3×D4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
1. C3×#5651C2semidirect
5. C32×#352C2semidirect
6. C3×#4476C2semidirect
7. C3×#4473C2semidirect
9. #69141C3direct (N × H)
30. #5651C2×C3semidirect
40. C3×#352D3semidirect
41. C3×#352C2×C3semidirect
42. #4476C2×C3semidirect
43. #4473C2×C3semidirect
154. #352C3×D3semidirect
417. C32#2201semidirect
478. C3#69141direct (N × H)
479. C3C3×#2201semidirect

Maximal subgroups

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

subgroupindex
C3×#56512
C3×#50532
C3×#47462
C3×#47422
C32×#3522
C3×#44762
C3×#44732
C3×#22013
#691413