Finite Group Databasebeta

← C3×#75971 #11803440

Subgroups — C3×#75971 #11803440

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic
2C2×C3×#892C211yesmaximal, characteristic
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C32×#389C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic
6C3×#4990C211yesmaximal, characteristic
7C3×#4980C211yesmaximal, characteristic, complemented
8C3×#4976C211yesmaximal, characteristic, complemented
9C3×#4976C211yesmaximal, characteristic, complemented
10C3×#4940C211yesmaximal, characteristic
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#4669C211yesmaximal, characteristic
13C3×#4667C211yesmaximal, characteristic
14C3×#4655C211yesmaximal, characteristic, complemented
15C3×#4646C211yesmaximal, characteristic, complemented
16C3×#2323—31nomaximal
17#75971C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#896C418yescomplemented
44C3×#892—24no—
45C3×#887—24no—
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C2×C3×C22⋊Q8—31no—
57C2×C3×C4×Q8—31no—
58C2×C3×#117—31no—
59C2×#896C2×C311yescharacteristic
60C2×#892C2×C311yescharacteristic
61C2×#887C2×C311yescharacteristic, complemented
62C3×#391—31no—
63C3×#389—21no—
64C3×#389—31no—
65C3×#389—31no—
66C3×#389D311yescharacteristic, complemented
67C3×#389C2×C311yescharacteristic, complemented
68C3×#388—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#387—31no—
73C3×#387—31no—
74C3×#380—31no—
75C3×C4×C4⋊C4—31no—
76#4990C2×C311yescharacteristic
77#4990C2×C311yescharacteristic
78#4980C2×C311yescharacteristic, complemented
79#4976C2×C311yescharacteristic, complemented
80#4976C2×C311yescharacteristic, complemented
81#4940C2×C311yescharacteristic
82C4×Dic3⋊C4C2×C311yescharacteristic, complemented
83#4669C2×C311yescharacteristic
84#4667C2×C311yescharacteristic
85#4655C2×C311yescharacteristic, complemented
86#4646C2×C311yescharacteristic, complemented
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3C2×C414yes—
105C2×C3×Dic6—22no—
106C2×C3×Dic6—22no—
107C2×C3×Dic6C2×C414yes—
108C32×C4⋊C4—22no—
109C32×C4⋊C4—22no—
110C32×C4⋊C4—41no—
111C32×C4⋊C4C2×C414yes—
112C32×C42—41no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—41no—
116C3×(C2×D3)⋊C4—41no—
117C3×(C2×D3)⋊C4C2×C414yes—
118C3×(C2×D3)⋊C4C2×C414yes—
119C3×C4⋊Dic3—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—41no—
124C3×Dic3⋊C4C2×C414yes—
125C3×Dic3⋊C4C2×C414yes—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3—41no—
130C3×C4×Dic3D414yes—
131#2323—31noSylow
132C22×C3×Q8—31no—
133C23×C3×C4—31no—
134C22×C4×D3C22×C311yescharacteristic
135C22×Dic6C22×C311yescharacteristic
136C3×C22⋊Q8—38no—
137C3×C4×Q8—64no—
138C3×#117—64no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C2×D311yescharacteristic
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C4⋊C4C22×C311yescharacteristic
155C2×C3×C4⋊C4C22×C311yescharacteristic
156C2×C3×C4⋊C4C22×C311yescharacteristic
157C2×C3×C4⋊C4C22×C311yescharacteristic
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—21no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×C3×C42—31no—
168C2×C3×C42—31no—
169C2×C3×C42—31no—
170C2×C3×C42C2×D311yescharacteristic
171C2×C3×C42C22×C311yescharacteristic
172C2×(C2×D3)⋊C4C22×C311yescharacteristic
173C2×(C2×D3)⋊C4C22×C311yescharacteristic
174C2×(C2×D3)⋊C4C22×C311yescharacteristic
175C2×(C2×D3)⋊C4C22×C311yescharacteristic
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
178C2×C4⋊Dic3C22×C311yescharacteristic
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C311yescharacteristic
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×Dic3⋊C4C22×C311yescharacteristic
185C2×C4×Dic3C22×C311yescharacteristic
186C2×C4×Dic3C22×C311yescharacteristic
187C2×C4×Dic3C22×C311yescharacteristic
188C2×C4×Dic3C22×C311yescharacteristic
189C2×C4×Dic3C22×C311yescharacteristic
190#896C3×C418yescomplemented
191#892—24no—
192#887—24no—
193C3×#95—21no—
194C3×#95—21no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95C2×D311yescharacteristic
204C3×#95C2×D311yescharacteristic
205C3×#95C22×C311yescharacteristic
206C3×#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C3⋊#95C22×C311yescharacteristic
215C23×C32C2411yescharacteristic
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3C22×C412yes—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C22×C412yes—
241C2×C32×C4C22×C412yes—
242C2×C32×C4C22×C412yes—
243C2×C32×C4C2×D412yes—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C22×C412yes—
260C2×C3×Dic3C22×C412yes—
261C2×C3×Dic3C22×C412yes—
262C2×C3×Dic3C2×D412yes—
263C2×C3×Dic3C2×D412yes—
264C2×C3×Dic3#4112yes—
265C3×C4×D3—28no—
266C3×Dic6—28no—
267C2×C22⋊Q8—31no—
268C2×C4×Q8—31no—
269C2×#117—31no—
270#391—31no—
271#389—31no—
272#389—31no—
273#389C3×D311yescharacteristic, complemented
274#388—31no—
275#388—31no—
276#388—31no—
277#388—31no—
278#387—31no—
279#387—31no—
280#380—31no—
281C4×C4⋊C4—31no—
282C24×C3—31no—
283C23×D3C23×C311yescharacteristic
284C2×C3×Q8—34no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—34no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—62no—
303C22×C3×C4—62no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C22×C3×C4C23×C311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C22×C3×C4C23×C311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×Dic3C23×C311yescharacteristic
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×C4×D3C2×C3×C414yes—
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6C2×C3×C414yes—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4—42no—
339C3×C4⋊C4—42no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—42no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—62no—
346C3×C4⋊C4—62no—
347C3×C4⋊C4—121no—
348C3×C4⋊C4C4×D314yes—
349C3×C4⋊C4C2×C3×C414yes—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C22⋊C4—121no—
355C3×C22⋊C4—121no—
356C3×C42—34no—
357C3×C42—41no—
358C3×C42—41no—
359C3×C42—42no—
360C3×C42—62no—
361C3×C42—62no—
362C3×C42—62no—
363C3×C42—121no—
364(C2×D3)⋊C4—22no—
365(C2×D3)⋊C4—22no—
366(C2×D3)⋊C4—41no—
367(C2×D3)⋊C4—41no—
368(C2×D3)⋊C4C2×C3×C414yes—
369(C2×D3)⋊C4C2×C3×C414yes—
370C4⋊Dic3—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—41no—
375Dic3⋊C4C2×C3×C414yes—
376Dic3⋊C4C2×C3×C414yes—
377C4×Dic3—22no—
378C4×Dic3—22no—
379C4×Dic3—22no—
380C4×Dic3—41no—
381C4×Dic3C3×D414yes—
382C22×C32C23×C411yescharacteristic
383C22×C32C22×D411yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32H(5,𝔽2)11yescharacteristic
386C22×C322−1+411yescharacteristic
387C22×C322−1+411yescharacteristic
388C22×C322−1+411yescharacteristic
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—22no—
399C32×C4—22no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4—41no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3C4×D414yes—
410C22×Q8—31no—
411C23×C4—31no—
412C22⋊Q8—38no—
413C4×Q8—64no—
414#117—64no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—31no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4C2×C3×D311yescharacteristic
423C2×C4⋊C4C2×C3×D311yescharacteristic
424C2×C4⋊C4C2×C3×D311yescharacteristic
425C2×C4⋊C4C2×C3×D311yescharacteristic
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—31no—
437C2×C42C2×C3×D311yescharacteristic
438#95—31no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—31no—
444#95—31no—
445#95—31no—
446#95C2×C3×D311yescharacteristic
447#95C2×C3×D311yescharacteristic
448C23×C3—21no—
449C23×C3—32no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3C23×D311yescharacteristic
457C23×C3C24×C311yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3C22×C3×C412yes—
465C3×Q8—68no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—68no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4C2×C4×D312yes—
544C2×C3×C4C2×C4×D312yes—
545C2×C3×C4C2×C4×D312yes—
546C2×C3×C4D3×D412yes—
547C2×C3×C4C22×C3×C412yes—
548C2×C3×C4C22×C3×C412yes—
549C2×C3×C4C22×C3×C412yes—
550C2×C3×C4C2×C3×D412yes—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3C22×C3×C412yes—
567C2×Dic3C22×C3×C412yes—
568C2×Dic3C22×C3×C412yes—
569C2×Dic3C2×C3×D412yes—
570C2×Dic3C2×C3×D412yes—
571C2×Dic3C3×#4112yes—
572C4×D3—28no—
573Dic6—28no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#51911yescharacteristic
576C2×C32#52011yescharacteristic
577C2×C32#53611yescharacteristic
578C2×C32#53711yescharacteristic
579C2×C32#54111yescharacteristic
580C2×C32#54211yescharacteristic
581C3×D3—42no—
582C24—31no—
583C2×Q8—34no—
584C2×Q8—62no—
585C2×Q8—62no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—34no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4C22×C3×D311yescharacteristic
597C22×C4C22×C3×D311yescharacteristic
598C22×C4C22×C3×D311yescharacteristic
599C22×C4C22×C3×D311yescharacteristic
600C22×C4C22×C3×D311yescharacteristic
601C22×C4C22×C3×D311yescharacteristic
602C22×C4C22×C3×D311yescharacteristic
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—34no—
606C4⋊C4—34no—
607C4⋊C4—41no—
608C4⋊C4—62no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—62no—
612C4⋊C4—121no—
613C4⋊C4C3×C4×D314yes—
614C22⋊C4—34no—
615C22⋊C4—34no—
616C22⋊C4—62no—
617C22⋊C4—62no—
618C22⋊C4—121no—
619C22⋊C4—121no—
620C42—34no—
621C42—41no—
622C42—62no—
623C42—62no—
624C42—62no—
625C42—121no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—62no—
634C22×C3—62no—
635C22×C3—62no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C22×C4×D311yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3#100411yescharacteristic
643C22×C3#100711yescharacteristic
644C22×C3#100711yescharacteristic
645C22×C3D3×#4111yescharacteristic
646C22×C3#101011yescharacteristic
647C22×C3C23×C3×C411yescharacteristic
648C22×C3C22×C3×D411yescharacteristic
649C22×C3C2×C3×#4111yescharacteristic
650C22×C3C3×H(5,𝔽2)11yescharacteristic
651C22×C3C3×2−1+411yescharacteristic
652C22×C3C3×2−1+411yescharacteristic
653C22×C3C3×2−1+411yescharacteristic
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C3×C4—24no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—22no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—34no—
671C3×C4—42no—
672C3×C4—42no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3C3×C4×D414yes—
696C32#232311yescharacteristic, complemented, Sylow
697C23—32no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23C23×C3×D311yescharacteristic
705Q8—68no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—68no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4C2×C3×C4×D312yes—
746C2×C4C2×C3×C4×D312yes—
747C2×C4C2×C3×C4×D312yes—
748C2×C4C3×D3×D412yes—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—122no—
757C2×C3#550411yescharacteristic
758C2×C3C4×D3×D411yescharacteristic
759C2×C3#557211yescharacteristic
760C2×C3#559711yescharacteristic
761C2×C3#564011yescharacteristic
762C2×C3#569611yescharacteristic
763C2×C3#572411yescharacteristic
764C2×C3C2×C3×C4×D411yescharacteristic
765C2×C3C3×#51911yescharacteristic
766C2×C3C3×#52011yescharacteristic
767C2×C3C3×#53611yescharacteristic
768C2×C3C3×#53711yescharacteristic
769C2×C3C3×#54111yescharacteristic
770C2×C3C3×#54211yescharacteristic
771D3—42no—
772C22—62no—
773C22—62no—
774C22—62no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22C22×C3×C4×D311yescharacteristic
780C22C2×C3×D3×D411yescharacteristic
781C22C3×#100411yescharacteristic
782C22C3×#100711yescharacteristic
783C22C3×#100711yescharacteristic
784C22C3×D3×#4111yescharacteristic
785C22C3×#101011yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—34no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—62no—
795C4—62no—
796C4—62no—
797C4—121no—
798C4—121no—
799C4—121no—
800C3—21no—
801C3#7597111yescharacteristic, direct product factor
802C3C3×#232311yescharacteristic, complemented
803C2—122no—
804C2C3×#550411yescharacteristic
805C2C3×C4×D3×D411yescharacteristic
806C2C3×#557211yescharacteristic
807C2C3×#559711yescharacteristic
808C2C3×#564011yescharacteristic
809C2C3×#569611yescharacteristic
810C2C3×#572411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#389C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#389D3
hypocenterC3C3×#2323
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
3. C2×C3×#887C2semidirect
4. C32×#389C2semidirect
7. C3×#4980C2semidirect
8. C3×#4976C2semidirect
9. C3×#4976C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
14. C3×#4655C2semidirect
15. C3×#4646C2semidirect
17. #75971C3direct (N × H)
43. C3×#896C4semidirect
61. C2×#887C2×C3semidirect
66. C3×#389D3semidirect
67. C3×#389C2×C3semidirect
78. #4980C2×C3semidirect
79. #4976C2×C3semidirect
80. #4976C2×C3semidirect
82. C4×Dic3⋊C4C2×C3semidirect
85. #4655C2×C3semidirect
86. #4646C2×C3semidirect
190. #896C3×C4semidirect
273. #389C3×D3semidirect
696. C32#2323semidirect
801. C3#75971direct (N × H)
802. C3C3×#2323semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C2×C3×#8922
C2×C3×#8872
C32×#3892
C3×#49902
C3×#49802
C3×#49762
C3×#49402
C3×C4×Dic3⋊C42
C3×#46692
C3×#46672
C3×#46552
C3×#46462
C3×#23233
#759713