Finite Group Databasebeta

← C3×#74385 #11803552

Subgroups — C3×#74385 #11803552

Order 1152.

1453 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic, complemented
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×C3×#884C211yesmaximal, characteristic
4C32×#385C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#4989C211yesmaximal, characteristic, complemented
7C3×#4988C211yesmaximal, characteristic, complemented
8C3×#4976C211yesmaximal, characteristic, complemented
9C3×#4957C211yesmaximal, characteristic, complemented
10C3×#4957C211yesmaximal, characteristic, complemented
11C3×#4951C211yesmaximal, characteristic, complemented
12C3×#4670C211yesmaximal, characteristic, complemented
13C3×#4667C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4649C211yesmaximal, characteristic, complemented
16C3×#2324—31nomaximal
17#74385C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C3×C4×#67—24no—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C2×C3×C4×Dic3C2211yescharacteristic
48C3×#892—24no—
49C3×#884C418yescomplemented
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C2×C3×#121—31no—
57C2×C3×C4×D4—31no—
58C2×C3×#117—31no—
59C2×C4×#67C2×C311yescharacteristic, complemented
60C2×#892C2×C311yescharacteristic, complemented
61C2×#884C2×C311yescharacteristic
62C3×#390—31no—
63C3×#390—31no—
64C3×#390—31no—
65C3×#389—31no—
66C3×#388—31no—
67C3×#388—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#385—21no—
71C3×#385—31no—
72C3×#385D311yescharacteristic, complemented
73C3×#385C2×C311yescharacteristic, complemented
74C3×#380—31no—
75C3×C4×C4⋊C4—31no—
76#5213C2×C311yescharacteristic, complemented
77#4989C2×C311yescharacteristic, complemented
78#4988C2×C311yescharacteristic, complemented
79#4976C2×C311yescharacteristic, complemented
80#4957C2×C311yescharacteristic, complemented
81#4957C2×C311yescharacteristic, complemented
82#4951C2×C311yescharacteristic, complemented
83#4670C2×C311yescharacteristic, complemented
84#4667C2×C311yescharacteristic, complemented
85#4665C2×C311yescharacteristic, complemented
86#4649C2×C311yescharacteristic, complemented
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4—41no—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67C2×C414yes—
104C2×C3×#67C2×C414yescomplemented
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×D12—41no—
112C2×C3×D12—41no—
113C2×C3×D12C2×C414yescomplemented
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3—41no—
119C2×C3×C4×D3C2×C414yescomplemented
120C32×C4⋊C4—22no—
121C32×C4⋊C4—41no—
122C32×C22⋊C4—41no—
123C32×C22⋊C4C2×C414yescomplemented
124C3×#217—22no—
125C3×#217—41no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×(C2×D3)⋊C4—41no—
132C3×(C2×D3)⋊C4—41no—
133C3×(C2×D3)⋊C4C2×C414yescomplemented
134C3×C4⋊Dic3—22no—
135C3×Dic3⋊C4—22no—
136C3×Dic3⋊C4—22no—
137C3×Dic3⋊C4—41no—
138C3×Dic3⋊C4C2×C414yescomplemented
139C3×C4×Dic3—22no—
140C3×C4×Dic3—41no—
141C3×C4×Dic3—41no—
142C3×C4×Dic3D414yescomplemented
143#2324—31noSylow
144C22×C3×D4—31no—
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—21no—
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4C2×D311yescharacteristic
151C23×C3×C4C22×C311yescharacteristic
152C22×#67C22×C311yescharacteristic
153C22×#67C22×C311yescharacteristic
154C22×D12C22×C311yescharacteristic
155C22×C4×D3C22×C311yescharacteristic
156C22×C4×D3C22×C311yescharacteristic
157C3×#121—38no—
158C3×C4×D4—64no—
159C3×#117—64no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4C2×D311yescharacteristic
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C22×C311yescharacteristic
170C2×C3×C4⋊C4C22×C311yescharacteristic
171C2×C3×C22⋊C4—21no—
172C2×C3×C22⋊C4—21no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C22⋊C4C22×C311yescharacteristic
186C2×C3×C22⋊C4C22×C311yescharacteristic
187C2×C3×C42—31no—
188C2×C3×C42—31no—
189C2×C3×C42—31no—
190C2×C3×C42—31no—
191C2×#217C22×C311yescharacteristic
192C2×#217C22×C311yescharacteristic
193C4×#67—24no—
194C2×(C2×D3)⋊C4C22×C311yescharacteristic
195C2×(C2×D3)⋊C4C22×C311yescharacteristic
196C2×(C2×D3)⋊C4C22×C311yescharacteristic
197C2×(C2×D3)⋊C4C22×C311yescharacteristic
198C2×(C2×D3)⋊C4C22×C311yescharacteristic
199C2×(C2×D3)⋊C4C22×C311yescharacteristic
200C2×(C2×D3)⋊C4C22×C311yescharacteristic
201C2×(C2×D3)⋊C4C22×C311yescharacteristic
202C2×C4⋊Dic3C22×C311yescharacteristic
203C2×Dic3⋊C4C22×C311yescharacteristic
204C2×Dic3⋊C4C22×C311yescharacteristic
205C2×Dic3⋊C4C22×C311yescharacteristic
206C2×Dic3⋊C4C22×C311yescharacteristic
207C2×C4×Dic3C22×C311yescharacteristic
208C2×C4×Dic3C22×C311yescharacteristic
209C2×C4×Dic3C22×C311yescharacteristic
210C2×C4×Dic3C22×C311yescharacteristic
211#892—24no—
212#884C3×C418yescomplemented
213C3×#95—21no—
214C3×#95—21no—
215C3×#95—31no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95C2×D311yescharacteristic
220C3×#95C2×D311yescharacteristic
221C3×#95C22×C311yescharacteristic
222C3×#95C22×C311yescharacteristic
223C3⋊#95C22×C311yescharacteristic
224C3⋊#95C22×C311yescharacteristic
225C3⋊#95C22×C311yescharacteristic
226C3⋊#95C22×C311yescharacteristic
227C23×C32—21no—
228C23×C32—21no—
229C23×C32—21no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32C22×C412yes—
234C23×C32C2411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
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—21no—
264C2×C32×C4—44no—
265C2×C32×C4C22×C412yes—
266C2×C32×C4C22×C412yes—
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×Dic3C22×C412yes—
284C2×C3×Dic3C22×C412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288C3×D12—44no—
289C3×C4×D3—28no—
290C3×C4×D3—44no—
291C2×#121—31no—
292C2×C4×D4—31no—
293C2×#117—31no—
294#390—31no—
295#390—31no—
296#390—31no—
297#389—31no—
298#388—31no—
299#388—31no—
300#386—31no—
301#386—31no—
302#385—31no—
303#385C3×D311yescharacteristic, complemented
304#380—31no—
305C4×C4⋊C4—31no—
306C24×C3—21no—
307C24×C3—31no—
308C24×C3—31no—
309C24×C3C22×D311yescharacteristic
310C24×C3C23×C311yescharacteristic
311C23×D3C23×C311yescharacteristic
312C23×D3C23×C311yescharacteristic
313C2×C3×D4—34no—
314C2×C3×D4—34no—
315C2×C3×D4—34no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—121no—
319C2×C3×D4—121no—
320C2×C3×D4—121no—
321C2×C3×D4—121no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—34no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—42no—
338C22×C3×C4—41no—
339C22×C3×C4—41no—
340C22×C3×C4—41no—
341C22×C3×C4—41no—
342C22×C3×C4—42no—
343C22×C3×C4—42no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—121no—
348C22×C3×C4—121no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C23×C311yescharacteristic
356C22×C3×C4C23×C311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C22×C3×C4C23×C311yescharacteristic
359C22×C3×C4C23×C311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C2×#67—22no—
362C2×#67—22no—
363C2×#67—41no—
364C2×#67—41no—
365C2×#67C2×C3×C414yes—
366C2×#67C2×C3×C414yescomplemented
367C22×Dic3C23×C311yescharacteristic
368C22×Dic3C23×C311yescharacteristic
369C22×Dic3C23×C311yescharacteristic
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C22×Dic3C23×C311yescharacteristic
373C2×D12—41no—
374C2×D12—41no—
375C2×D12C2×C3×C414yescomplemented
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—41no—
380C2×C4×D3—41no—
381C2×C4×D3C2×C3×C414yescomplemented
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—34no—
385C3×C4⋊C4—42no—
386C3×C4⋊C4—41no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—42no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—62no—
391C3×C4⋊C4—62no—
392C3×C4⋊C4—121no—
393C3×C22⋊C4—24no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—42no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—121no—
403C3×C22⋊C4—121no—
404C3×C22⋊C4—121no—
405C3×C22⋊C4—121no—
406C3×C22⋊C4—121no—
407C3×C22⋊C4C4×D314yescomplemented
408C3×C22⋊C4C2×C3×C414yescomplemented
409C3×C42—34no—
410C3×C42—62no—
411C3×C42—121no—
412C3×C42—121no—
413#217—22no—
414#217—41no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—41no—
419(C2×D3)⋊C4—41no—
420(C2×D3)⋊C4—41no—
421(C2×D3)⋊C4—41no—
422(C2×D3)⋊C4C2×C3×C414yescomplemented
423C4⋊Dic3—22no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—41no—
427Dic3⋊C4C2×C3×C414yescomplemented
428C4×Dic3—22no—
429C4×Dic3—41no—
430C4×Dic3—41no—
431C4×Dic3C3×D414yescomplemented
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32C23×C411yescharacteristic
440C22×C32C22×D411yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C32H(5,𝔽2)11yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C322−1+411yescharacteristic
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—22no—
463C32×C4—41no—
464C32×C4—41no—
465C32×C4—41no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3C4×D414yes—
472C22×D4—31no—
473C22×D4—31no—
474C22×D4—31no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4C2×C3×D311yescharacteristic
478#121—38no—
479C4×D4—64no—
480#117—64no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4C2×C3×D311yescharacteristic
487C2×C4⋊C4C2×C3×D311yescharacteristic
488C2×C22⋊C4—31no—
489C2×C22⋊C4—31no—
490C2×C22⋊C4—31no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4C2×C3×D311yescharacteristic
499C2×C22⋊C4C2×C3×D311yescharacteristic
500C2×C42—31no—
501C2×C42—31no—
502C2×C42—31no—
503C2×C42—31no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95—31no—
508#95C2×C3×D311yescharacteristic
509#95C2×C3×D311yescharacteristic
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—22no—
526C23×C3—32no—
527C23×C3—32no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3C2×C4×D312yes—
545C23×C3C22×C3×C412yes—
546C23×C3C23×D311yescharacteristic
547C23×C3C24×C311yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3C22×C3×C412yes—
561C22×D3C22×C3×C412yes—
562C3×D4—68no—
563C3×D4—124no—
564C3×D4—124no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—22no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
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—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—44no—
619C2×C3×C4—44no—
620C2×C3×C4—48no—
621C2×C3×C4—68no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—124no—
636C2×C3×C4C2×C4×D312yes—
637C2×C3×C4C2×C4×D312yes—
638C2×C3×C4D3×D412yes—
639C2×C3×C4C22×C3×C412yes—
640C2×C3×C4C22×C3×C412yes—
641C2×C3×C4C2×C3×D412yes—
642#67—28no—
643#67—44no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3C22×C3×C412yes—
658C2×Dic3C22×C3×C412yes—
659C2×Dic3C2×C3×D412yes—
660C2×Dic3C2×C3×D412yes—
661C2×Dic3C3×#4112yes—
662D12—44no—
663C4×D3—28no—
664C4×D3—44no—
665C2×C32—42no—
666C2×C32C2×C4×D411yescharacteristic
667C2×C32#51811yescharacteristic
668C2×C32#52011yescharacteristic
669C2×C32#53511yescharacteristic
670C2×C32#53711yescharacteristic
671C2×C32#54011yescharacteristic
672C2×C32#54211yescharacteristic
673C3×D3—42no—
674C3×D3—42no—
675C24—31no—
676C24—31no—
677C24C22×C3×D311yescharacteristic
678C2×D4—34no—
679C2×D4—34no—
680C2×D4—34no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—121no—
684C2×D4—121no—
685C2×D4—121no—
686C2×D4—121no—
687C22×C4—22no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—34no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—121no—
701C22×C4—121no—
702C22×C4C22×C3×D311yescharacteristic
703C22×C4C22×C3×D311yescharacteristic
704C22×C4C22×C3×D311yescharacteristic
705C22×C4C22×C3×D311yescharacteristic
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D311yescharacteristic
708C4⋊C4—22no—
709C4⋊C4—34no—
710C4⋊C4—41no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—121no—
715C22⋊C4—34no—
716C22⋊C4—41no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—121no—
722C22⋊C4—121no—
723C22⋊C4—121no—
724C22⋊C4—121no—
725C22⋊C4—121no—
726C22⋊C4C3×C4×D314yescomplemented
727C42—34no—
728C42—62no—
729C42—121no—
730C42—121no—
731C22×C3—24no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3C22×C4×D311yescharacteristic
774C22×C3C2×D3×D411yescharacteristic
775C22×C3#100411yescharacteristic
776C22×C3#100411yescharacteristic
777C22×C3#100711yescharacteristic
778C22×C3D3×#4111yescharacteristic
779C22×C3#100911yescharacteristic
780C22×C3C23×C3×C411yescharacteristic
781C22×C3C22×C3×D411yescharacteristic
782C22×C3C2×C3×#4111yescharacteristic
783C22×C3C3×H(5,𝔽2)11yescharacteristic
784C22×C3C3×H(5,𝔽2)11yescharacteristic
785C22×C3C3×H(5,𝔽2)11yescharacteristic
786C22×C3C3×2−1+411yescharacteristic
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—34no—
808C3×C4—42no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—41no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—81no—
821C3×C4—81no—
822C3×C4—121no—
823C3×C4—121no—
824C3×C4—121no—
825Dic3—22no—
826Dic3—22no—
827Dic3—41no—
828Dic3—41no—
829Dic3—41no—
830Dic3C3×C4×D414yes—
831C32#232411yescharacteristic, complemented, Sylow
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—32no—
839C23—32no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23C2×C3×C4×D312yes—
853C23C23×C3×D311yescharacteristic
854D4—68no—
855D4—124no—
856D4—124no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—44no—
878C2×C4—68no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—124no—
893C2×C4C2×C3×C4×D312yes—
894C2×C4C2×C3×C4×D312yes—
895C2×C4C3×D3×D412yes—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—44no—
904C2×C3—42no—
905C2×C3—42no—
906C2×C3—122no—
907C2×C3—122no—
908C2×C3#550411yescharacteristic
909C2×C3C4×D3×D411yescharacteristic
910C2×C3#554511yescharacteristic
911C2×C3#559211yescharacteristic
912C2×C3#562911yescharacteristic
913C2×C3#564011yescharacteristic
914C2×C3#566311yescharacteristic
915C2×C3C2×C3×C4×D411yescharacteristic
916C2×C3C3×#51811yescharacteristic
917C2×C3C3×#52011yescharacteristic
918C2×C3C3×#53511yescharacteristic
919C2×C3C3×#53711yescharacteristic
920C2×C3C3×#54011yescharacteristic
921C2×C3C3×#54211yescharacteristic
922D3—42no—
923D3—42no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22C22×C3×C4×D311yescharacteristic
946C22C2×C3×D3×D411yescharacteristic
947C22C3×#100411yescharacteristic
948C22C3×#100411yescharacteristic
949C22C3×#100711yescharacteristic
950C22C3×D3×#4111yescharacteristic
951C22C3×#100911yescharacteristic
952C4—22no—
953C4—22no—
954C4—22no—
955C4—34no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—62no—
960C4—62no—
961C4—121no—
962C4—121no—
963C4—121no—
964C3—21no—
965C3#7438511yescharacteristic, direct product factor
966C3C3×#232411yescharacteristic, complemented
967C2—42no—
968C2—122no—
969C2—122no—
970C2C3×#550411yescharacteristic
971C2C3×C4×D3×D411yescharacteristic
972C2C3×#554511yescharacteristic
973C2C3×#559211yescharacteristic
974C2C3×#562911yescharacteristic
975C2C3×#564011yescharacteristic
976C2C3×#566311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC2×C3×#884C2
cosocleC23×C3C24×C3
hypercenterC3×#385D3
hypocenterC3C3×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#67C2semidirect
2. C2×C3×#892C2semidirect
4. C32×#385C2semidirect
5. C3×#5213C2semidirect
6. C3×#4989C2semidirect
7. C3×#4988C2semidirect
8. C3×#4976C2semidirect
9. C3×#4957C2semidirect
10. C3×#4957C2semidirect
11. C3×#4951C2semidirect
12. C3×#4670C2semidirect
13. C3×#4667C2semidirect
14. C3×#4665C2semidirect
15. C3×#4649C2semidirect
17. #74385C3direct (N × H)
49. C3×#884C4semidirect
59. C2×C4×#67C2×C3semidirect
60. C2×#892C2×C3semidirect
72. C3×#385D3semidirect
73. C3×#385C2×C3semidirect
76. #5213C2×C3semidirect
77. #4989C2×C3semidirect
78. #4988C2×C3semidirect
79. #4976C2×C3semidirect
80. #4957C2×C3semidirect
81. #4957C2×C3semidirect
82. #4951C2×C3semidirect
83. #4670C2×C3semidirect
84. #4667C2×C3semidirect
85. #4665C2×C3semidirect
86. #4649C2×C3semidirect
104. C2×C3×#67C2×C4semidirect
113. C2×C3×D12C2×C4semidirect
119. C2×C3×C4×D3C2×C4semidirect
123. C32×C22⋊C4C2×C4semidirect
133. C3×(C2×D3)⋊C4C2×C4semidirect
138. C3×Dic3⋊C4C2×C4semidirect
142. C3×C4×Dic3D4semidirect
212. #884C3×C4semidirect
303. #385C3×D3semidirect
366. C2×#67C2×C3×C4semidirect
375. C2×D12C2×C3×C4semidirect
381. C2×C4×D3C2×C3×C4semidirect
407. C3×C22⋊C4C4×D3semidirect
408. C3×C22⋊C4C2×C3×C4semidirect
422. (C2×D3)⋊C4C2×C3×C4semidirect
427. Dic3⋊C4C2×C3×C4semidirect
431. C4×Dic3C3×D4semidirect
726. C22⋊C4C3×C4×D3semidirect
831. C32#2324semidirect
965. C3#74385direct (N × H)
966. C3C3×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C3×#8922
C2×C3×#8842
C32×#3852
C3×#52132
C3×#49892
C3×#49882
C3×#49762
C3×#49572
C3×#49512
C3×#46702
C3×#46672
C3×#46652
C3×#46492
C3×#23243
#743853