Finite Group Databasebeta

← C3×#82273 #11808372

Subgroups — C3×#82273 #11808372

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C212yesmaximal, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#4994C212yesmaximal, complemented
5C3×#4991C211yesmaximal, characteristic, complemented
6C3×#4981C211yesmaximal, characteristic, complemented
7C3×#4961C212yesmaximal, complemented
8C3×#4960C211yesmaximal, characteristic
9C3×#4953C211yesmaximal, characteristic, complemented
10C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
11C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C3×#2392—31nomaximal
13#82273C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C32×#117—24no—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2212yes—
26C3×C4×#67—28no—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×C4×Dic3C2212yes—
35C3×C4×D12—24no—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×C4×D4—32no—
41C2×C3×C4×D4—31no—
42C2×C3×#117—21no—
43C2×C3×#117D311yescharacteristic, complemented
44C2×C3×#117C2×C311yescharacteristic, complemented
45C2×C4×#67C2×C312yescomplemented
46C2×C4×D12C2×C311yescharacteristic, complemented
47C3×#398—31no—
48C3×#397—31no—
49C3×#396—32no—
50C3×#394—31no—
51C3×#394—32no—
52C3×#392—31no—
53C3×C4×C4⋊C4—31no—
54C3×C4×C22⋊C4—32no—
55#4994C2×C312yescomplemented
56#4991C2×C311yescharacteristic, complemented
57#4981C2×C311yescharacteristic, complemented
58#4961C2×C312yescomplemented
59#4960C2×C311yescharacteristic
60#4953C2×C311yescharacteristic, complemented
61C4×(C2×D3)⋊C4C2×C312yescomplemented
62C4×C4⋊Dic3C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4D414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×D12—24no—
81C2×C3×D12—22no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—24no—
85C32×C4⋊C4—22no—
86C32×C4⋊C4—22no—
87C32×C22⋊C4—22no—
88C32×C22⋊C4—22no—
89C32×C42—22no—
90C32×C42D414yescomplemented
91C3×#217—24no—
92C3×(C2×D3)⋊C4—24no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—24no—
95C3×(C2×D3)⋊C4—24no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3—24no—
98C3×Dic3⋊C4—24no—
99C3×C4×Dic3—24no—
100#2392—31noSylow
101C22×C3×D4—32no—
102C22×C3×D4—31no—
103C23×C3×C4—21no—
104C23×C3×C4—32no—
105C23×C3×C4C2×D311yescharacteristic
106C23×C3×C4C22×C311yescharacteristic
107C22×#67C22×C312yes—
108C22×D12C22×C311yescharacteristic
109C22×C4×D3C22×C312yes—
110C3×C4×D4—68no—
111C3×C4×D4—64no—
112C3×#117—28no—
113C3×#117—24no—
114C3×#117—24no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C4⋊C4C22×C311yescharacteristic
123C2×C3×C4⋊C4C22×C311yescharacteristic
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4C2×D311yescharacteristic
132C2×C3×C22⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C22×C311yescharacteristic
134C2×C3×C22⋊C4C22×C311yescharacteristic
135C2×C3×C42—21no—
136C2×C3×C42—21no—
137C2×C3×C42—32no—
138C2×C3×C42C2×D311yescharacteristic
139C2×C3×C42C2×D311yescharacteristic
140C2×C3×C42C22×C311yescharacteristic
141C2×C3×C42C22×C311yescharacteristic
142C2×#217C22×C312yes—
143C4×#67—28no—
144C2×(C2×D3)⋊C4C22×C312yes—
145C2×(C2×D3)⋊C4C22×C312yes—
146C2×(C2×D3)⋊C4C22×C312yes—
147C2×(C2×D3)⋊C4C22×C312yes—
148C2×C4⋊Dic3C22×C312yes—
149C2×C4⋊Dic3C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C312yes—
151C2×C4×Dic3C22×C312yes—
152C4×D12—24no—
153C3×#95—32no—
154C3×#95—32no—
155C3×#95—31no—
156C3×#95—31no—
157C3⋊#95C22×C311yescharacteristic
158C3⋊#95C22×C311yescharacteristic
159C3⋊#95C22×C312yes—
160C3⋊#95C22×C312yes—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32C2×D412yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3#4114yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—28no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4C2×D412yes—
188C2×C32×C4#4112yes—
189C3×#67—216no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3#4114yes—
199C3×D12—28no—
200C3×C4×D3—48no—
201C2×C4×D4—32no—
202C2×C4×D4—31no—
203C2×#117C3×D311yescharacteristic, complemented
204#398—31no—
205#397—31no—
206#396—32no—
207#394—31no—
208#394—32no—
209#392—31no—
210C4×C4⋊C4—31no—
211C4×C22⋊C4—32no—
212C24×C3—21no—
213C24×C3—32no—
214C24×C3C22×D311yescharacteristic
215C24×C3C23×C311yescharacteristic
216C23×D3C23×C312yes—
217C2×C3×D4—64no—
218C2×C3×D4—64no—
219C2×C3×D4—64no—
220C2×C3×D4—64no—
221C2×C3×D4—62no—
222C22×C3×C4—24no—
223C22×C3×C4—24no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—32no—
237C22×C3×C4—32no—
238C22×C3×C4—64no—
239C22×C3×C4—64no—
240C22×C3×C4—64no—
241C22×C3×C4D1214yescomplemented
242C22×C3×C4C3×D414yescomplemented
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C23×C311yescharacteristic
250C22×C3×C4C23×C311yescharacteristic
251C22×C3×C4C23×C311yescharacteristic
252C22×C3×C4C23×C311yescharacteristic
253C22×C3×C4C23×C311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C2×#67—24no—
256C2×#67—24no—
257C2×#67—24no—
258C22×Dic3C23×C312yes—
259C22×Dic3C23×C312yes—
260C22×Dic3C23×C312yes—
261C2×D12—24no—
262C2×D12—22no—
263C2×C4×D3—24no—
264C2×C4×D3—24no—
265C2×C4×D3—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—64no—
273C3×C4⋊C4—64no—
274C3×C4⋊C4—62no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—64no—
282C3×C22⋊C4—64no—
283C3×C22⋊C4—64no—
284C3×C22⋊C4—64no—
285C3×C22⋊C4—64no—
286C3×C42—24no—
287C3×C42—22no—
288C3×C42—22no—
289C3×C42—24no—
290C3×C42—64no—
291C3×C42#6714yescomplemented
292C3×C42C3×D414yescomplemented
293#217—24no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—24no—
297(C2×D3)⋊C4—24no—
298C4⋊Dic3—22no—
299C4⋊Dic3—24no—
300Dic3⋊C4—24no—
301C4×Dic3—24no—
302C22×C32—22no—
303C22×C32—24no—
304C22×C32—41no—
305C22×C32—42no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C2×#4111yescharacteristic
310C22×C32C2×#4112yes—
311C22×C32C2×#4112yes—
312C2×C3×D3—24no—
313C2×C3×D3—24no—
314C2×C3×D3—24no—
315C2×C3×D3—42no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C32×C4—22no—
320C32×C4—22no—
321C32×C4—22no—
322C32×C4—41no—
323C32×C4—41no—
324C32×C4#12114yes—
325C3×Dic3—24no—
326C3×Dic3—42no—
327C3×Dic3—42no—
328C22×D4—32no—
329C22×D4—31no—
330C23×C4—32no—
331C23×C4C2×C3×D311yescharacteristic
332C4×D4—68no—
333C4×D4—64no—
334#117—24no—
335C2×C4⋊C4—32no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—32no—
338C2×C4⋊C4C2×C3×D311yescharacteristic
339C2×C4⋊C4C2×C3×D311yescharacteristic
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—32no—
344C2×C22⋊C4—32no—
345C2×C22⋊C4C2×C3×D311yescharacteristic
346C2×C22⋊C4C2×C3×D311yescharacteristic
347C2×C42—32no—
348C2×C42C2×C3×D311yescharacteristic
349C2×C42C2×C3×D311yescharacteristic
350#95—32no—
351#95—32no—
352#95—31no—
353#95—31no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—21no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—22no—
366C23×C3—34no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—62no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3C2×D1212yes—
376C23×C3C2×C3×D412yes—
377C23×C3C23×D311yescharacteristic
378C23×C3C24×C311yescharacteristic
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3C3×#4114yes—
386C3×D4—68no—
387C3×D4—616no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—216no—
391C2×C3×C4—21no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—28no—
400C2×C3×C4—28no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—34no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—128no—
431C2×C3×C4C2×D1212yes—
432C2×C3×C4C2×D1212yes—
433C2×C3×C4#23512yes—
434C2×C3×C4C2×#6712yes—
435C2×C3×C4C2×#6712yes—
436C2×C3×C4C2×#6712yes—
437C2×C3×C4C2×C3×D412yes—
438C2×C3×C4C2×C3×D412yes—
439C2×C3×C4C2×C3×D412yes—
440C2×C3×C4C2×C3×D412yes—
441C2×C3×C4C2×C3×D412yes—
442C2×C3×C4C3×#4112yes—
443#67—216no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3C3×#4114yes—
453D12—28no—
454C4×D3—48no—
455C2×C32—42no—
456C2×C32C2×#12111yescharacteristic
457C2×C32#52512yes—
458C2×C32#52511yescharacteristic
459C2×C32#52912yes—
460C2×C32#53211yescharacteristic
461C3×D3—44no—
462C24—32no—
463C24C22×C3×D311yescharacteristic
464C2×D4—64no—
465C2×D4—64no—
466C2×D4—64no—
467C2×D4—64no—
468C2×D4—62no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—64no—
475C22×C4—64no—
476C22×C4—64no—
477C22×C4C3×D1214yescomplemented
478C22×C4C22×C3×D311yescharacteristic
479C22×C4C22×C3×D311yescharacteristic
480C22×C4C22×C3×D311yescharacteristic
481C22×C4C22×C3×D311yescharacteristic
482C22×C4C22×C3×D311yescharacteristic
483C22×C4C22×C3×D311yescharacteristic
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—64no—
487C4⋊C4—64no—
488C4⋊C4—62no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—64no—
492C22⋊C4—64no—
493C22⋊C4—64no—
494C22⋊C4—64no—
495C22⋊C4—64no—
496C42—22no—
497C42—64no—
498C42C3×#6714yescomplemented
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—24no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—42no—
518C22×C3—41no—
519C22×C3—64no—
520C22×C3—64no—
521C22×C3—64no—
522C22×C3—122no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3C22×D1211yescharacteristic
527C22×C3C2×#23511yescharacteristic
528C22×C3D3×#4112yes—
529C22×C3D3×#4112yes—
530C22×C3C22×#6711yescharacteristic
531C22×C3C22×C3×D411yescharacteristic
532C22×C3C22×C3×D411yescharacteristic
533C22×C3C2×C3×#4111yescharacteristic
534C22×C3C2×C3×#4112yes—
535C22×C3C2×C3×#4112yes—
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—42no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—42no—
543C3×C4—24no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—24no—
551C3×C4—42no—
552C3×C4—42no—
553C3×C4—42no—
554C3×C4—42no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—64no—
560C3×C4—122no—
561C3×C4—122no—
562C3×C4#93014yes—
563C3×C4C3×#12114yes—
564Dic3—24no—
565Dic3—42no—
566Dic3—42no—
567C32#239211yescharacteristic, complemented, Sylow
568C23—21no—
569C23—22no—
570C23—22no—
571C23—21no—
572C23—34no—
573C23—62no—
574C23—62no—
575C23—62no—
576C23—62no—
577C23—62no—
578C23—62no—
579C23C2×C3×D1212yes—
580C23C23×C3×D311yescharacteristic
581D4—68no—
582D4—616no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—28no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—34no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—128no—
602C2×C4C2×C3×D1212yes—
603C2×C4C2×C3×D1212yes—
604C2×C4C3×#23512yes—
605C2×C4C2×C3×#6712yes—
606C2×C4C2×C3×#6712yes—
607C2×C4C2×C3×#6712yes—
608C2×C3—22no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—44no—
614C2×C3—42no—
615C2×C3—42no—
616C2×C3—124no—
617C2×C3#552412yes—
618C2×C3#552812yes—
619C2×C3C2×#93011yescharacteristic
620C2×C3#582811yescharacteristic
621C2×C3#583211yescharacteristic
622C2×C3C2×C3×#12111yescharacteristic
623C2×C3C3×#52512yes—
624C2×C3C3×#52511yescharacteristic
625C2×C3C3×#52912yes—
626C2×C3C3×#53211yescharacteristic
627D3—44no—
628C22—24no—
629C22—22no—
630C22—42no—
631C22—41no—
632C22—41no—
633C22—64no—
634C22—64no—
635C22—64no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22C22×C3×D1211yescharacteristic
641C22C2×C3×#23511yescharacteristic
642C22C3×D3×#4112yes—
643C22C3×D3×#4112yes—
644C22C22×C3×#6711yescharacteristic
645C4—22no—
646C4—22no—
647C4—22no—
648C4—41no—
649C4—41no—
650C4—64no—
651C4—122no—
652C4—122no—
653C4C3×#93014yes—
654C3—21no—
655C3#8227311yescharacteristic, direct product factor
656C3C3×#239211yescharacteristic, complemented
657C2—42no—
658C2—124no—
659C2C3×#552412yes—
660C2C3×#552812yes—
661C2C2×C3×#93011yescharacteristic
662C2C3×#582811yescharacteristic
663C2C3×#583211yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC3×#4960C2
hypercenterC2×C3×#117D3
hypocenterC3C3×#2392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#4994C2semidirect
5. C3×#4991C2semidirect
6. C3×#4981C2semidirect
7. C3×#4961C2semidirect
9. C3×#4953C2semidirect
10. C3×C4×(C2×D3)⋊C4C2semidirect
11. C3×C4×C4⋊Dic3C2semidirect
13. #82273C3direct (N × H)
43. C2×C3×#117D3semidirect
44. C2×C3×#117C2×C3semidirect
45. C2×C4×#67C2×C3semidirect
46. C2×C4×D12C2×C3semidirect
55. #4994C2×C3semidirect
56. #4991C2×C3semidirect
57. #4981C2×C3semidirect
58. #4961C2×C3semidirect
60. #4953C2×C3semidirect
61. C4×(C2×D3)⋊C4C2×C3semidirect
62. C4×C4⋊Dic3C2×C3semidirect
67. C22×C32×C4D4semidirect
90. C32×C42D4semidirect
203. C2×#117C3×D3semidirect
241. C22×C3×C4D12semidirect
242. C22×C3×C4C3×D4semidirect
291. C3×C42#67semidirect
292. C3×C42C3×D4semidirect
477. C22×C4C3×D12semidirect
498. C42C3×#67semidirect
567. C32#2392semidirect
655. C3#82273direct (N × H)
656. C3C3×#2392semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×C4×#672
C2×C3×C4×D122
C3×#49942
C3×#49912
C3×#49812
C3×#49612
C3×#49602
C3×#49532
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
C3×#23923
#822733