Finite Group Databasebeta

← C3×#82327 #11803637

Subgroups — C3×#82327 #11803637

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4989C211yesmaximal, characteristic, complemented
9C3×#4978C211yesmaximal, characteristic, complemented
10C3×#4958C211yesmaximal, characteristic, complemented
11C3×#4956C211yesmaximal, characteristic, complemented
12C3×#4944C211yesmaximal, characteristic, complemented
13C3×#4942C211yesmaximal, characteristic, complemented
14C3×#4940C211yesmaximal, characteristic, complemented
15C3×#4933C211yesmaximal, characteristic, complemented
16C3×#2325—31nomaximal
17#82327C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C32×C4×D4—24no—
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C42C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C3×#939C418yescomplemented
36C3×C4×#67—24no—
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#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×#121—31no—
57C2×C3×C4×D4—21no—
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4D311yescharacteristic, complemented
60C2×C3×C4×D4C2×C311yescharacteristic, complemented
61C2×#939C2×C311yescharacteristic
62C2×C4×#67C2×C311yescharacteristic, complemented
63C3×#388—31no—
64C3×#388—31no—
65C3×#387—31no—
66C3×#387—31no—
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#386—31no—
71C3×#385—31no—
72C3×#385—31no—
73C3×#380—31no—
74C2×C3×#95—31no—
75#5220C2×C311yescharacteristic, complemented
76#5213C2×C311yescharacteristic, complemented
77#5210C2×C311yescharacteristic, complemented
78C2×C3⋊#95C2×C311yescharacteristic, complemented
79#4989C2×C311yescharacteristic, complemented
80#4978C2×C311yescharacteristic, complemented
81#4958C2×C311yescharacteristic, complemented
82#4956C2×C311yescharacteristic, complemented
83#4944C2×C311yescharacteristic, complemented
84#4942C2×C311yescharacteristic, complemented
85#4940C2×C311yescharacteristic, complemented
86#4933C2×C311yescharacteristic, complemented
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C2×C32×D4—22no—
91C2×C32×D4—22no—
92C2×C32×D4C2×C414yescomplemented
93C22×C32×C4—22no—
94C22×C32×C4—41no—
95C22×C32×C4—41no—
96C22×C32×C4—41no—
97C22×C32×C4—41no—
98C22×C32×C4D414yescomplemented
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67C2×C414yescomplemented
109C2×C3×#67C2×C414yescomplemented
110C22×C3×Dic3—22no—
111C22×C3×Dic3—41no—
112C22×C3×Dic3—41no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3—41no—
115C22×C3×Dic3C2×C414yescomplemented
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—41no—
125C2×C3×C4×D3—41no—
126C32×C4⋊C4—22no—
127C32×C22⋊C4—22no—
128C32×C22⋊C4—22no—
129C32×C42—22no—
130C3×#217—22no—
131C3×#217—41no—
132C3×#217—41no—
133C3×#217C2×C414yescomplemented
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4C2×C414yescomplemented
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—41no—
140C3×Dic3⋊C4—41no—
141C3×Dic3⋊C4C2×C414yescomplemented
142C3×C4×Dic3—22no—
143#2325—31noSylow
144C22×C3×D4—21no—
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C22×C311yescharacteristic
149C23×C3×C4—21no—
150C23×C3×C4—21no—
151C23×C3×C4—31no—
152C23×C3×C4—31no—
153C23×C3×C4—31no—
154C23×C3×C4C2×D311yescharacteristic
155C23×C3×C4C2×D311yescharacteristic
156C23×C3×C4C22×C311yescharacteristic
157C23×C3×C4C22×C311yescharacteristic
158C22×#67C22×C311yescharacteristic
159C22×#67C22×C311yescharacteristic
160C23×Dic3C22×C311yescharacteristic
161C23×Dic3C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C3×#121—38no—
164C3×C4×D4—28no—
165C3×C4×D4—24no—
166C3×C4×D4—24no—
167C3×C4×D4—64no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4C2×D311yescharacteristic
174C2×C3×C4⋊C4C22×C311yescharacteristic
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4C2×D311yescharacteristic
186C2×C3×C22⋊C4C2×D311yescharacteristic
187C2×C3×C22⋊C4C22×C311yescharacteristic
188C2×C3×C22⋊C4C22×C311yescharacteristic
189C2×C3×C42—21no—
190C2×C3×C42—31no—
191C2×C3×C42C2×D311yescharacteristic
192C2×C3×C42C22×C311yescharacteristic
193C2×#217C22×C311yescharacteristic
194C2×#217C22×C311yescharacteristic
195C2×#217C22×C311yescharacteristic
196C2×#217C22×C311yescharacteristic
197#939C3×C418yescomplemented
198C4×#67—24no—
199C2×(C2×D3)⋊C4C22×C311yescharacteristic
200C2×(C2×D3)⋊C4C22×C311yescharacteristic
201C2×(C2×D3)⋊C4C22×C311yescharacteristic
202C2×(C2×D3)⋊C4C22×C311yescharacteristic
203C2×Dic3⋊C4C22×C311yescharacteristic
204C2×Dic3⋊C4C22×C311yescharacteristic
205C2×Dic3⋊C4C22×C311yescharacteristic
206C2×Dic3⋊C4C22×C311yescharacteristic
207C2×C4×Dic3C22×C311yescharacteristic
208C3×#95—31no—
209C3×#95—31no—
210C3×#95—31no—
211C3×#95—31no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3⋊#95C22×C311yescharacteristic
219C3⋊#95C22×C311yescharacteristic
220C3⋊#95C22×C311yescharacteristic
221C3⋊#95C22×C311yescharacteristic
222C3⋊#95C22×C311yescharacteristic
223C3⋊#95C22×C311yescharacteristic
224C3⋊#95C22×C311yescharacteristic
225C3⋊#95C22×C311yescharacteristic
226C3⋊#95C22×C311yescharacteristic
227C3⋊#95C22×C311yescharacteristic
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32C22×C412yes—
239C23×C32C22×C412yes—
240C23×C32C2×D412yes—
241C23×C32#4112yes—
242C23×C32C2411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C22×C412yes—
250C32×D4—28no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—44no—
264C2×C32×C4—44no—
265C2×C32×C4C22×C412yes—
266C2×C32×C4C2×D412yes—
267C2×C32×C4C2×D412yes—
268C3×#67—28no—
269C3×#67—44no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—44no—
289C2×C3×Dic3—44no—
290C2×C3×Dic3C22×C412yes—
291C2×C3×Dic3C22×C412yes—
292C2×C3×Dic3C22×C412yes—
293C3×C4×D3—44no—
294C2×#121—31no—
295C2×C4×D4—31no—
296C2×C4×D4C3×D311yescharacteristic, complemented
297#388—31no—
298#388—31no—
299#387—31no—
300#387—31no—
301#386—31no—
302#386—31no—
303#386—31no—
304#386—31no—
305#385—31no—
306#385—31no—
307#380—31no—
308C2×#95—31no—
309C24×C3—21no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C24×C3C23×C311yescharacteristic
315C24×C3C23×C311yescharacteristic
316C23×D3C23×C311yescharacteristic
317C2×C3×D4—24no—
318C2×C3×D4—24no—
319C2×C3×D4—22no—
320C2×C3×D4—22no—
321C2×C3×D4—22no—
322C2×C3×D4—22no—
323C2×C3×D4—24no—
324C2×C3×D4—34no—
325C2×C3×D4—34no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—121no—
329C2×C3×D4—121no—
330C2×C3×D4C4×D314yescomplemented
331C2×C3×D4C2×C3×C414yescomplemented
332C22×C3×C4—24no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—24no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—34no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—41no—
352C22×C3×C4—41no—
353C22×C3×C4—41no—
354C22×C3×C4—41no—
355C22×C3×C4—41no—
356C22×C3×C4—41no—
357C22×C3×C4—42no—
358C22×C3×C4—42no—
359C22×C3×C4—42no—
360C22×C3×C4—42no—
361C22×C3×C4—62no—
362C22×C3×C4—62no—
363C22×C3×C4—121no—
364C22×C3×C4—121no—
365C22×C3×C4—121no—
366C22×C3×C4—121no—
367C22×C3×C4—121no—
368C22×C3×C4—121no—
369C22×C3×C4#6714yescomplemented
370C22×C3×C4C3×D414yescomplemented
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C23×C311yescharacteristic
377C22×C3×C4C23×C311yescharacteristic
378C22×C3×C4C23×C311yescharacteristic
379C22×C3×C4C23×C311yescharacteristic
380C22×C3×C4C23×C311yescharacteristic
381C2×#67—22no—
382C2×#67—22no—
383C2×#67—41no—
384C2×#67—41no—
385C2×#67C2×C3×C414yescomplemented
386C2×#67C2×C3×C414yescomplemented
387C22×Dic3—22no—
388C22×Dic3—41no—
389C22×Dic3—41no—
390C22×Dic3—41no—
391C22×Dic3—41no—
392C22×Dic3C2×C3×C414yescomplemented
393C22×Dic3C23×C311yescharacteristic
394C22×Dic3C23×C311yescharacteristic
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C22×Dic3C23×C311yescharacteristic
399C22×Dic3C23×C311yescharacteristic
400C2×C4×D3—22no—
401C2×C4×D3—41no—
402C2×C4×D3—41no—
403C3×C4⋊C4—24no—
404C3×C4⋊C4—22no—
405C3×C4⋊C4—22no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—62no—
408C3×C4⋊C4—121no—
409C3×C4⋊C4—121no—
410C3×C22⋊C4—24no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—22no—
413C3×C22⋊C4—22no—
414C3×C22⋊C4—22no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—121no—
421C3×C22⋊C4—121no—
422C3×C22⋊C4—121no—
423C3×C22⋊C4—121no—
424C3×C42—24no—
425C3×C42—22no—
426C3×C42—22no—
427C3×C42—62no—
428#217—22no—
429#217—41no—
430#217—41no—
431#217C2×C3×C414yescomplemented
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—41no—
434(C2×D3)⋊C4—41no—
435(C2×D3)⋊C4C2×C3×C414yescomplemented
436Dic3⋊C4—22no—
437Dic3⋊C4—41no—
438Dic3⋊C4—41no—
439Dic3⋊C4C2×C3×C414yescomplemented
440C4×Dic3—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C4×D414yes—
455C22×C32C23×C411yescharacteristic
456C22×C32C22×D411yescharacteristic
457C22×C32C2×#4111yescharacteristic
458C22×C32H(5,𝔽2)11yescharacteristic
459C22×C32H(5,𝔽2)11yescharacteristic
460C22×C32H(5,𝔽2)11yescharacteristic
461C22×C322−1+411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—22no—
472C32×C4—41no—
473C32×C4—41no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C22×D4—31no—
482C22×D4—31no—
483C22×D4C2×C3×D311yescharacteristic
484C23×C4—31no—
485C23×C4—31no—
486C23×C4—31no—
487C23×C4C2×C3×D311yescharacteristic
488C23×C4C2×C3×D311yescharacteristic
489#121—38no—
490C4×D4—24no—
491C4×D4—64no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4C2×C3×D311yescharacteristic
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4C2×C3×D311yescharacteristic
506C2×C22⋊C4C2×C3×D311yescharacteristic
507C2×C42—31no—
508C2×C42C2×C3×D311yescharacteristic
509#95—31no—
510#95—31no—
511#95—31no—
512#95—31no—
513#95—31no—
514#95—31no—
515#95—31no—
516#95—31no—
517#95—31no—
518#95—31no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—32no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—41no—
552C23×C3—41no—
553C23×C3—41no—
554C23×C3—41no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3C2×C4×D312yes—
562C23×C3C2×C4×D312yes—
563C23×C3#23512yes—
564C23×C3C2×#6712yes—
565C23×C3C22×C3×C412yes—
566C23×C3C22×C3×C412yes—
567C23×C3C2×C3×D412yes—
568C23×C3C3×#4112yes—
569C23×C3C23×D311yescharacteristic
570C23×C3C24×C311yescharacteristic
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3C22×C3×C412yes—
578C3×D4—216no—
579C3×D4—28no—
580C3×D4—28no—
581C3×D4—68no—
582C3×D4—124no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—44no—
626C2×C3×C4—44no—
627C2×C3×C4—48no—
628C2×C3×C4—48no—
629C2×C3×C4—44no—
630C2×C3×C4—44no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—124no—
650C2×C3×C4—124no—
651C2×C3×C4—124no—
652C2×C3×C4C2×C4×D312yes—
653C2×C3×C4C2×#6712yes—
654C2×C3×C4C2×#6712yes—
655C2×C3×C4C22×C3×C412yes—
656C2×C3×C4C2×C3×D412yes—
657C2×C3×C4C2×C3×D412yes—
658#67—28no—
659#67—44no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—44no—
679C2×Dic3—44no—
680C2×Dic3C22×C3×C412yes—
681C2×Dic3C22×C3×C412yes—
682C2×Dic3C22×C3×C412yes—
683C4×D3—44no—
684C2×C32—24no—
685C2×C32—42no—
686C2×C32C2×C4×D411yescharacteristic
687C2×C32#51811yescharacteristic
688C2×C32#52011yescharacteristic
689C2×C32#53411yescharacteristic
690C2×C32#53711yescharacteristic
691C2×C32#53811yescharacteristic
692C2×C32#53911yescharacteristic
693C3×D3—42no—
694C24—31no—
695C24C22×C3×D311yescharacteristic
696C24C22×C3×D311yescharacteristic
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—34no—
700C2×D4—34no—
701C2×D4—62no—
702C2×D4—62no—
703C2×D4—121no—
704C2×D4—121no—
705C2×D4C3×C4×D314yescomplemented
706C22×C4—22no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—34no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—41no—
716C22×C4—41no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—62no—
720C22×C4—62no—
721C22×C4—121no—
722C22×C4—121no—
723C22×C4—121no—
724C22×C4—121no—
725C22×C4—121no—
726C22×C4—121no—
727C22×C4C3×#6714yescomplemented
728C22×C4C22×C3×D311yescharacteristic
729C22×C4C22×C3×D311yescharacteristic
730C22×C4C22×C3×D311yescharacteristic
731C22×C4C22×C3×D311yescharacteristic
732C22×C4C22×C3×D311yescharacteristic
733C4⋊C4—22no—
734C4⋊C4—34no—
735C4⋊C4—62no—
736C4⋊C4—121no—
737C4⋊C4—121no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C42—22no—
749C42—62no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—24no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—24no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—42no—
787C22×C3—42no—
788C22×C3—42no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3C4×#6714yes—
805C22×C3C3×C4×D414yes—
806C22×C3C22×C4×D311yescharacteristic
807C22×C3C2×#23511yescharacteristic
808C22×C3#100411yescharacteristic
809C22×C3#100411yescharacteristic
810C22×C3#100911yescharacteristic
811C22×C3#101011yescharacteristic
812C22×C3C22×#6711yescharacteristic
813C22×C3C23×C3×C411yescharacteristic
814C22×C3C22×C3×D411yescharacteristic
815C22×C3C2×C3×#4111yescharacteristic
816C22×C3C3×H(5,𝔽2)11yescharacteristic
817C22×C3C3×H(5,𝔽2)11yescharacteristic
818C22×C3C3×H(5,𝔽2)11yescharacteristic
819C22×C3C3×2−1+411yescharacteristic
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—41no—
827C3×C4—24no—
828C3×C4—24no—
829C3×C4—22no—
830C3×C4—22no—
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—22no—
835C3×C4—42no—
836C3×C4—42no—
837C3×C4—42no—
838C3×C4—41no—
839C3×C4—41no—
840C3×C4—41no—
841C3×C4—41no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—62no—
845C3×C4—121no—
846C3×C4—121no—
847C3×C4—121no—
848C3×C4—121no—
849Dic3—22no—
850Dic3—22no—
851Dic3—22no—
852Dic3—41no—
853Dic3—41no—
854Dic3—41no—
855Dic3—41no—
856C32#232511yescharacteristic, complemented, Sylow
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—32no—
868C23—61no—
869C23—61no—
870C23—61no—
871C23—61no—
872C23—61no—
873C23—61no—
874C23C2×C3×C4×D312yes—
875C23C2×C3×C4×D312yes—
876C23C3×#23512yes—
877C23C2×C3×#6712yes—
878C23C23×C3×D311yescharacteristic
879D4—28no—
880D4—68no—
881D4—124no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—124no—
918C2×C4—124no—
919C2×C4—124no—
920C2×C4C2×C3×C4×D312yes—
921C2×C4C2×C3×#6712yes—
922C2×C4C2×C3×#6712yes—
923C2×C3—24no—
924C2×C3—24no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—44no—
933C2×C3—44no—
934C2×C3—42no—
935C2×C3—42no—
936C2×C3—122no—
937C2×C3#554511yescharacteristic
938C2×C3#554611yescharacteristic
939C2×C3#556011yescharacteristic
940C2×C3#556411yescharacteristic
941C2×C3C2×C4×#6711yescharacteristic
942C2×C3#580411yescharacteristic
943C2×C3#583311yescharacteristic
944C2×C3C2×C3×C4×D411yescharacteristic
945C2×C3C3×#51811yescharacteristic
946C2×C3C3×#52011yescharacteristic
947C2×C3C3×#53411yescharacteristic
948C2×C3C3×#53711yescharacteristic
949C2×C3C3×#53811yescharacteristic
950C2×C3C3×#53911yescharacteristic
951D3—42no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—62no—
966C22—62no—
967C22—62no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22C3×C4×#6714yes—
973C22C22×C3×C4×D311yescharacteristic
974C22C2×C3×#23511yescharacteristic
975C22C3×#100411yescharacteristic
976C22C3×#100411yescharacteristic
977C22C3×#100911yescharacteristic
978C22C3×#101011yescharacteristic
979C22C22×C3×#6711yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—41no—
984C4—41no—
985C4—62no—
986C4—62no—
987C4—62no—
988C4—121no—
989C4—121no—
990C4—121no—
991C4—121no—
992C3—21no—
993C3#8232711yescharacteristic, direct product factor
994C3C3×#232511yescharacteristic, complemented
995C2—24no—
996C2—42no—
997C2—122no—
998C2C3×#554511yescharacteristic
999C2C3×#554611yescharacteristic
1000C2C3×#556011yescharacteristic
1001C2C3×#556411yescharacteristic
1002C2C2×C3×C4×#6711yescharacteristic
1003C2C3×#580411yescharacteristic
1004C2C3×#583311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#939C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2325
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C3×#5220C2semidirect
5. C3×#5213C2semidirect
6. C3×#5210C2semidirect
7. C2×C3×C3⋊#95C2semidirect
8. C3×#4989C2semidirect
9. C3×#4978C2semidirect
10. C3×#4958C2semidirect
11. C3×#4956C2semidirect
12. C3×#4944C2semidirect
13. C3×#4942C2semidirect
14. C3×#4940C2semidirect
15. C3×#4933C2semidirect
17. #82327C3direct (N × H)
35. C3×#939C4semidirect
59. C2×C3×C4×D4D3semidirect
60. C2×C3×C4×D4C2×C3semidirect
62. C2×C4×#67C2×C3semidirect
75. #5220C2×C3semidirect
76. #5213C2×C3semidirect
77. #5210C2×C3semidirect
78. C2×C3⋊#95C2×C3semidirect
79. #4989C2×C3semidirect
80. #4978C2×C3semidirect
81. #4958C2×C3semidirect
82. #4956C2×C3semidirect
83. #4944C2×C3semidirect
84. #4942C2×C3semidirect
85. #4940C2×C3semidirect
86. #4933C2×C3semidirect
92. C2×C32×D4C2×C4semidirect
98. C22×C32×C4D4semidirect
108. C2×C3×#67C2×C4semidirect
109. C2×C3×#67C2×C4semidirect
115. C22×C3×Dic3C2×C4semidirect
133. C3×#217C2×C4semidirect
137. C3×(C2×D3)⋊C4C2×C4semidirect
141. C3×Dic3⋊C4C2×C4semidirect
197. #939C3×C4semidirect
296. C2×C4×D4C3×D3semidirect
330. C2×C3×D4C4×D3semidirect
331. C2×C3×D4C2×C3×C4semidirect
369. C22×C3×C4#67semidirect
370. C22×C3×C4C3×D4semidirect
385. C2×#67C2×C3×C4semidirect
386. C2×#67C2×C3×C4semidirect
392. C22×Dic3C2×C3×C4semidirect
431. #217C2×C3×C4semidirect
435. (C2×D3)⋊C4C2×C3×C4semidirect
439. Dic3⋊C4C2×C3×C4semidirect
705. C2×D4C3×C4×D3semidirect
727. C22×C4C3×#67semidirect
856. C32#2325semidirect
993. C3#82327direct (N × H)
994. C3C3×#2325semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9392
C2×C3×C4×#672
C3×#52202
C3×#52132
C3×#52102
C2×C3×C3⋊#952
C3×#49892
C3×#49782
C3×#49582
C3×#49562
C3×#49442
C3×#49422
C3×#49402
C3×#49332
C3×#23253
#823273