Finite Group Databasebeta

← C3×#75460 #11803446

Subgroups — C3×#75460 #11803446

Order 1152.

1207 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic
2C2×C3×#877C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C32×#388C211yesmaximal, characteristic
5C3×#4976C211yesmaximal, characteristic, complemented
6C3×#4972C211yesmaximal, characteristic, complemented
7C3×#4951C211yesmaximal, characteristic
8C3×#4944C211yesmaximal, characteristic
9C3×#4944C211yesmaximal, characteristic
10C3×#4942C211yesmaximal, characteristic
11C3×#4933C211yesmaximal, characteristic, complemented
12C3×#4653C211yesmaximal, characteristic, complemented
13C3×#4649C211yesmaximal, characteristic, complemented
14C3×#4647C211yesmaximal, characteristic, complemented
15C3×#4646C211yesmaximal, characteristic, complemented
16C3×#2323—31nomaximal
17#75460C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
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×#878C418yescomplemented
44C3×#877—24no—
45C3×C4×Dic6—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×#878C2×C311yescharacteristic
60C2×#877C2×C311yescharacteristic
61C2×C4×Dic6C2×C311yescharacteristic, complemented
62C3×#391—31no—
63C3×#389—31no—
64C3×#389—31no—
65C3×#389—31no—
66C3×#388—21no—
67C3×#388—31no—
68C3×#388—31no—
69C3×#388—31no—
70C3×#388D311yescharacteristic
71C3×#388C2×C311yescharacteristic
72C3×#387—31no—
73C3×#387—31no—
74C3×#380—31no—
75C3×C4×C4⋊C4—31no—
76#4976C2×C311yescharacteristic, complemented
77#4972C2×C311yescharacteristic, complemented
78#4951C2×C311yescharacteristic
79#4944C2×C311yescharacteristic
80#4944C2×C311yescharacteristic
81#4942C2×C311yescharacteristic
82#4933C2×C311yescharacteristic, complemented
83#4653C2×C311yescharacteristic, complemented
84#4649C2×C311yescharacteristic, complemented
85#4647C2×C311yescharacteristic, complemented
86#4646C2×C311yescharacteristic, complemented
87C24×C32C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3—22no—
95C22×C3×Dic3—22no—
96C22×C3×Dic3C2×C414yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C2×C3×Dic6—22no—
106C2×C3×Dic6—22no—
107C2×C3×Dic6C2×C414yes—
108C32×C4⋊C4—41no—
109C32×C22⋊C4—22no—
110C32×C22⋊C4—41no—
111C32×C22⋊C4C2×C414yes—
112C32×C42—22no—
113C3×#217—22no—
114C3×#217—41no—
115C3×#217C2×C414yes—
116C3×C4⋊Dic3—22no—
117C3×C4⋊Dic3C2×C414yes—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—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—41no—
129C3×C4×Dic3—41no—
130C3×C4×Dic3D414yes—
131#2323—31noSylow
132C22×C3×Q8—31no—
133C23×C3×C4—31no—
134C23×Dic3C22×C311yescharacteristic
135C22×Dic6C22×C311yescharacteristic
136C3×C22⋊Q8—38no—
137C3×C4×Q8—64no—
138C3×#117—64no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
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⋊C4C22×C311yescharacteristic
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C22×C311yescharacteristic
162C2×C3×C22⋊C4C22×C311yescharacteristic
163C2×C3×C22⋊C4C22×C311yescharacteristic
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×#217C22×C311yescharacteristic
173C2×#217C22×C311yescharacteristic
174C2×#217C22×C311yescharacteristic
175C2×C4⋊Dic3C22×C311yescharacteristic
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×Dic3⋊C4C22×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#878C3×C418yescomplemented
191#877—24no—
192C4×Dic6—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×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32C22×C412yes—
222C23×C32C2411yescharacteristic
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×C4C22×C412yes—
239C2×C32×C4C22×C412yes—
240C2×C32×C4C2×D412yes—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—28no—
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×Dic3C22×C412yes—
263C2×C3×Dic3C2×D412yes—
264C2×C3×Dic3C2×D412yes—
265C2×C3×Dic3#4112yes—
266C3×Dic6—28no—
267C2×C22⋊Q8—31no—
268C2×C4×Q8—31no—
269C2×#117—31no—
270#391—31no—
271#389—31no—
272#389—31no—
273#389—31no—
274#388—31no—
275#388—31no—
276#388—31no—
277#388C3×D311yescharacteristic
278#387—31no—
279#387—31no—
280#380—31no—
281C4×C4⋊C4—31no—
282C24×C3—21no—
283C24×C3C22×D311yescharacteristic
284C24×C3C23×C311yescharacteristic
285C2×C3×Q8—34no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
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—34no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—62no—
304C22×C3×C4—62no—
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×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3C2×C3×C414yes—
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C311yescharacteristic
327C22×Dic3C23×C311yescharacteristic
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6C2×C3×C414yes—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—34no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C4⋊C4—62no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—121no—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—22no—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—42no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—121no—
354C3×C22⋊C4C4×D314yes—
355C3×C22⋊C4C2×C3×C414yes—
356C3×C42—22no—
357C3×C42—22no—
358C3×C42—34no—
359C3×C42—42no—
360C3×C42—62no—
361C3×C42—62no—
362C3×C42—121no—
363C3×C42—121no—
364#217—22no—
365#217—41no—
366#217C2×C3×C414yes—
367C4⋊Dic3—22no—
368C4⋊Dic3C2×C3×C414yes—
369Dic3⋊C4—22no—
370Dic3⋊C4—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—41no—
380C4×Dic3—41no—
381C4×Dic3C3×D414yes—
382C22×C32—22no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32C23×C411yescharacteristic
390C22×C32C22×D411yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32H(5,𝔽2)11yescharacteristic
393C22×C322−1+411yescharacteristic
394C22×C322−1+411yescharacteristic
395C22×C322−1+411yescharacteristic
396C32×C4—22no—
397C32×C4—22no—
398C32×C4—22no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—41no—
402C3×Dic3—22no—
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⋊C4—31no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4C2×C3×D311yescharacteristic
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—31no—
429C2×C22⋊C4C2×C3×D311yescharacteristic
430C2×C22⋊C4C2×C3×D311yescharacteristic
431C2×C22⋊C4C2×C3×D311yescharacteristic
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—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—22no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3C2×C4×D312yes—
469C23×C3C22×C3×C412yes—
470C23×C3C23×D311yescharacteristic
471C23×C3C24×C311yescharacteristic
472C3×Q8—68no—
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—21no—
485C2×C3×C4—22no—
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—21no—
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—32no—
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—41no—
528C2×C3×C4—68no—
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×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4C2×C4×D312yes—
547C2×C3×C4C2×C4×D312yes—
548C2×C3×C4D3×D412yes—
549C2×C3×C4C22×C3×C412yes—
550C2×C3×C4C22×C3×C412yes—
551C2×C3×C4C2×C3×D412yes—
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—28no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3C22×C3×C412yes—
571C2×Dic3C22×C3×C412yes—
572C2×Dic3C22×C3×C412yes—
573C2×Dic3C22×C3×C412yes—
574C2×Dic3C2×C3×D412yes—
575C2×Dic3C2×C3×D412yes—
576C2×Dic3C3×#4112yes—
577Dic6—28no—
578C2×C32—42no—
579C2×C32C2×C4×D411yescharacteristic
580C2×C32#51911yescharacteristic
581C2×C32#52011yescharacteristic
582C2×C32#53611yescharacteristic
583C2×C32#53711yescharacteristic
584C2×C32#54111yescharacteristic
585C2×C32#54211yescharacteristic
586C24C22×C3×D311yescharacteristic
587C2×Q8—34no—
588C2×Q8—62no—
589C2×Q8—62no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—34no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—62no—
600C22×C4—62no—
601C22×C4C22×C3×D311yescharacteristic
602C22×C4C22×C3×D311yescharacteristic
603C22×C4C22×C3×D311yescharacteristic
604C22×C4C22×C3×D311yescharacteristic
605C22×C4C22×C3×D311yescharacteristic
606C22×C4C22×C3×D311yescharacteristic
607C4⋊C4—34no—
608C4⋊C4—34no—
609C4⋊C4—34no—
610C4⋊C4—41no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—62no—
617C4⋊C4—121no—
618C22⋊C4—22no—
619C22⋊C4—34no—
620C22⋊C4—41no—
621C22⋊C4—62no—
622C22⋊C4—121no—
623C22⋊C4C3×C4×D314yes—
624C42—22no—
625C42—34no—
626C42—62no—
627C42—62no—
628C42—121no—
629C42—121no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3C22×C4×D311yescharacteristic
659C22×C3C2×D3×D411yescharacteristic
660C22×C3#100411yescharacteristic
661C22×C3D3×#4111yescharacteristic
662C22×C3#101011yescharacteristic
663C22×C3#101011yescharacteristic
664C22×C3#101011yescharacteristic
665C22×C3C23×C3×C411yescharacteristic
666C22×C3C22×C3×D411yescharacteristic
667C22×C3C2×C3×#4111yescharacteristic
668C22×C3C3×H(5,𝔽2)11yescharacteristic
669C22×C3C3×2−1+411yescharacteristic
670C22×C3C3×2−1+411yescharacteristic
671C22×C3C3×2−1+411yescharacteristic
672C3×C4—22no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—34no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—81no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3C3×C4×D414yes—
706C32#232311yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23C2×C3×C4×D312yes—
714C23C23×C3×D311yescharacteristic
715Q8—68no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
737C2×C4—32no—
738C2×C4—68no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4C2×C3×C4×D312yes—
757C2×C4C2×C3×C4×D312yes—
758C2×C4C3×D3×D412yes—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—82no—
769C2×C3#551611yescharacteristic
770C2×C3C4×D3×D411yescharacteristic
771C2×C3#554611yescharacteristic
772C2×C3#560811yescharacteristic
773C2×C3#564811yescharacteristic
774C2×C3#566911yescharacteristic
775C2×C3#570111yescharacteristic
776C2×C3C2×C3×C4×D411yescharacteristic
777C2×C3C3×#51911yescharacteristic
778C2×C3C3×#52011yescharacteristic
779C2×C3C3×#53611yescharacteristic
780C2×C3C3×#53711yescharacteristic
781C2×C3C3×#54111yescharacteristic
782C2×C3C3×#54211yescharacteristic
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22C22×C3×C4×D311yescharacteristic
791C22C2×C3×D3×D411yescharacteristic
792C22C3×#100411yescharacteristic
793C22C3×D3×#4111yescharacteristic
794C22C3×#101011yescharacteristic
795C22C3×#101011yescharacteristic
796C22C3×#101011yescharacteristic
797C4—22no—
798C4—22no—
799C4—22no—
800C4—34no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—62no—
805C4—62no—
806C4—62no—
807C4—62no—
808C4—121no—
809C4—121no—
810C4—121no—
811C3—21no—
812C3#7546011yescharacteristic, direct product factor
813C3C3×#232311yescharacteristic, complemented
814C2—42no—
815C2C3×#551611yescharacteristic
816C2C3×C4×D3×D411yescharacteristic
817C2C3×#554611yescharacteristic
818C2C3×#560811yescharacteristic
819C2C3×#564811yescharacteristic
820C2C3×#566911yescharacteristic
821C2C3×#570111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×#2323
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×Dic6C2semidirect
5. C3×#4976C2semidirect
6. C3×#4972C2semidirect
11. C3×#4933C2semidirect
12. C3×#4653C2semidirect
13. C3×#4649C2semidirect
14. C3×#4647C2semidirect
15. C3×#4646C2semidirect
17. #75460C3direct (N × H)
43. C3×#878C4semidirect
61. C2×C4×Dic6C2×C3semidirect
76. #4976C2×C3semidirect
77. #4972C2×C3semidirect
82. #4933C2×C3semidirect
83. #4653C2×C3semidirect
84. #4649C2×C3semidirect
85. #4647C2×C3semidirect
86. #4646C2×C3semidirect
190. #878C3×C4semidirect
706. C32#2323semidirect
812. C3#75460direct (N × H)
813. C3C3×#2323semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
C2×C3×#8772
C2×C3×C4×Dic62
C32×#3882
C3×#49762
C3×#49722
C3×#49512
C3×#49442
C3×#49422
C3×#49332
C3×#46532
C3×#46492
C3×#46472
C3×#46462
C3×#23233
#754603