Finite Group Databasebeta

← C3×#82404 #11810279

Subgroups — C3×#82404 #11810279

Order 1152.

1813 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×#929C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6C3×#5213C211yesmaximal, characteristic, complemented
7C3×#5210C211yesmaximal, characteristic, complemented
8C3×#4993C211yesmaximal, characteristic, complemented
9C3×#4992C211yesmaximal, characteristic, complemented
10C3×#4959C211yesmaximal, characteristic, complemented
11C3×#4959C211yesmaximal, characteristic, complemented
12C3×#4955C211yesmaximal, characteristic, complemented
13C3×#4942C211yesmaximal, characteristic, complemented
14C3×#4940C211yesmaximal, characteristic, complemented
15C3×#4940C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#82404C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C32×C4×D4—24no—
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×C32×C42C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic, complemented
33C2×C3×#217C2211yescharacteristic, complemented
34C3×#937—24no—
35C3×#929—24no—
36C2×C3×(C2×D3)⋊C4—24no—
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C2×C3×#123—31no—
58C2×C3×#120—31no—
59C2×C3×C4×D4—21no—
60C2×C3×C4×D4D311yescharacteristic, complemented
61C2×C3×C4×D4C2×C311yescharacteristic, complemented
62C22×C3×C22⋊C4—31no—
63C2×#937C2×C311yescharacteristic
64C2×#929C2×C311yescharacteristic, complemented
65C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
66C3×#399—31no—
67C3×#397—31no—
68C3×#394—31no—
69C3×#394—31no—
70C3×#388—31no—
71C3×#388—31no—
72C3×#386—31no—
73C3×#386—31no—
74C3×#385—31no—
75C3×#380—31no—
76C3×#379—31no—
77#5220C2×C311yescharacteristic, complemented
78#5213C2×C311yescharacteristic, complemented
79#5210C2×C311yescharacteristic, complemented
80#4993C2×C311yescharacteristic, complemented
81#4992C2×C311yescharacteristic, complemented
82#4959C2×C311yescharacteristic, complemented
83#4959C2×C311yescharacteristic, complemented
84#4955C2×C311yescharacteristic, complemented
85#4942C2×C311yescharacteristic, complemented
86#4940C2×C311yescharacteristic, complemented
87#4940C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C24×C32C2311yescharacteristic
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3—41no—
96C23×C3×D3—41no—
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4D414yes—
102C22×C32×C4—22no—
103C22×C32×C4—22no—
104C22×C32×C4—22no—
105C22×C32×C4—22no—
106C22×C32×C4—41no—
107C22×C32×C4—41no—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67—41no—
118C2×C3×#67—41no—
119C22×C3×Dic3—22no—
120C22×C3×Dic3—22no—
121C22×C3×Dic3—41no—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C32×C4⋊C4—22no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—22no—
131C32×C42—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×#217—41no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—41no—
144C3×(C2×D3)⋊C4—41no—
145C3×(C2×D3)⋊C4D414yescomplemented
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—22no—
148C3×Dic3⋊C4—41no—
149C3×Dic3⋊C4—41no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—21no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C22×C311yescharacteristic
158C23×C3×C4—21no—
159C23×C3×C4—21no—
160C23×C3×C4—31no—
161C23×C3×C4C2×D311yescharacteristic
162C23×C3×C4C2×D311yescharacteristic, complemented
163C23×C3×C4C22×C311yescharacteristic
164C23×C3×C4C22×C311yescharacteristic, complemented
165C22×#67C22×C311yescharacteristic
166C22×#67C22×C311yescharacteristic
167C23×Dic3C22×C311yescharacteristic
168C3×#123—64no—
169C3×#120—64no—
170C3×C4×D4—28no—
171C3×C4×D4—24no—
172C3×C4×D4—24no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
179C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
180C2×C3×C22⋊C4—21no—
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—64no—
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
199C2×C3×C22⋊C4C22×C311yescharacteristic
200C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
201C2×C3×C42—21no—
202C2×C3×C42C2×D311yescharacteristic, complemented
203C2×C3×C42C22×C311yescharacteristic, complemented
204C2×#217C22×C311yescharacteristic
205C2×#217C22×C311yescharacteristic
206C2×#217C22×C311yescharacteristic, complemented
207C2×#217C22×C311yescharacteristic, complemented
208#937—24no—
209#929—24no—
210C2×(C2×D3)⋊C4—24no—
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic
214C2×(C2×D3)⋊C4C22×C311yescharacteristic
215C2×(C2×D3)⋊C4C22×C311yescharacteristic
216C2×(C2×D3)⋊C4C22×C311yescharacteristic
217C2×(C2×D3)⋊C4C22×C311yescharacteristic
218C2×(C2×D3)⋊C4C22×C311yescharacteristic
219C2×(C2×D3)⋊C4C22×C311yescharacteristic
220C2×(C2×D3)⋊C4C22×C311yescharacteristic
221C2×Dic3⋊C4C22×C311yescharacteristic, complemented
222C2×Dic3⋊C4C22×C311yescharacteristic, complemented
223C2×Dic3⋊C4C22×C311yescharacteristic, complemented
224C2×Dic3⋊C4C22×C311yescharacteristic, complemented
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95—31no—
231C3⋊#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C3⋊#95C22×C311yescharacteristic, complemented
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—21no—
247C23×C32C2×D412yes—
248C23×C32C2×D412yes—
249C23×C32#4112yes—
250C23×C32#4112yes—
251C23×C32C2411yescharacteristic
252C22×C3×D3—28no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3—44no—
270C22×C3×D3—44no—
271C22×C3×D3C2×D412yes—
272C22×C3×D3#4112yes—
273C32×D4—28no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—44no—
288C2×C32×C4—44no—
289C2×C32×C4C2×D412yes—
290C2×C32×C4C2×D412yes—
291C3×#67—44no—
292C3×#67—44no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—44no—
311C2×C3×Dic3C2×D412yes—
312C2×#123—31no—
313C2×#120—31no—
314C2×C4×D4C3×D311yescharacteristic, complemented
315C22×C22⋊C4—31no—
316#399—31no—
317#397—31no—
318#394—31no—
319#394—31no—
320#388—31no—
321#388—31no—
322#386—31no—
323#386—31no—
324#385—31no—
325#380—31no—
326#379—31no—
327C24×C3—21no—
328C24×C3—21no—
329C24×C3—31no—
330C24×C3—31no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—62no—
336C24×C3—121no—
337C24×C3—121no—
338C24×C3C22×D311yescharacteristic
339C24×C3C22×D311yescharacteristic
340C24×C3C23×C311yescharacteristic
341C24×C3C23×C311yescharacteristic
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—22no—
345C23×D3—22no—
346C23×D3—22no—
347C23×D3—41no—
348C23×D3—41no—
349C23×D3C23×C311yescharacteristic
350C23×D3C23×C311yescharacteristic
351C2×C3×D4—24no—
352C2×C3×D4—24no—
353C2×C3×D4—22no—
354C2×C3×D4—22no—
355C2×C3×D4—22no—
356C2×C3×D4—22no—
357C2×C3×D4—24no—
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—62no—
361C2×C3×D4—62no—
362C2×C3×D4—121no—
363C2×C3×D4—121no—
364C2×C3×D4#6714yes—
365C2×C3×D4C3×D414yes—
366C22×C3×C4—24no—
367C22×C3×C4—24no—
368C22×C3×C4—22no—
369C22×C3×C4—22no—
370C22×C3×C4—22no—
371C22×C3×C4—22no—
372C22×C3×C4—22no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—22no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—21no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—42no—
388C22×C3×C4—42no—
389C22×C3×C4—41no—
390C22×C3×C4—41no—
391C22×C3×C4—41no—
392C22×C3×C4—41no—
393C22×C3×C4—42no—
394C22×C3×C4—42no—
395C22×C3×C4—62no—
396C22×C3×C4—62no—
397C22×C3×C4—121no—
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C23×C311yescharacteristic
404C22×C3×C4C23×C311yescharacteristic
405C22×C3×C4C23×C311yescharacteristic
406C22×C3×C4C23×C311yescharacteristic
407C22×C3×C4C23×C311yescharacteristic
408C2×#67—22no—
409C2×#67—22no—
410C2×#67—22no—
411C2×#67—22no—
412C2×#67—41no—
413C2×#67—41no—
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—41no—
417C22×Dic3C23×C311yescharacteristic
418C22×Dic3C23×C311yescharacteristic
419C22×Dic3C23×C311yescharacteristic
420C22×Dic3C23×C311yescharacteristic
421C22×Dic3C23×C311yescharacteristic
422C22×Dic3C23×C311yescharacteristic
423C3×C4⋊C4—24no—
424C3×C4⋊C4—22no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—62no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—121no—
429C3×C4⋊C4—121no—
430C3×C22⋊C4—24no—
431C3×C22⋊C4—24no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—62no—
443C3×C22⋊C4—62no—
444C3×C22⋊C4—62no—
445C3×C22⋊C4—62no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—121no—
448C3×C22⋊C4—121no—
449C3×C22⋊C4—121no—
450C3×C42—24no—
451C3×C42—22no—
452C3×C42—22no—
453#217—22no—
454#217—22no—
455#217—22no—
456#217—41no—
457(C2×D3)⋊C4—22no—
458(C2×D3)⋊C4—22no—
459(C2×D3)⋊C4—22no—
460(C2×D3)⋊C4—22no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—41no—
465(C2×D3)⋊C4—41no—
466(C2×D3)⋊C4C3×D414yescomplemented
467Dic3⋊C4—22no—
468Dic3⋊C4—22no—
469Dic3⋊C4—41no—
470Dic3⋊C4—41no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—41no—
481C22×C32—41no—
482C22×C32—41no—
483C22×C32—41no—
484C22×C32#12314yescomplemented
485C22×C32C22×D411yescharacteristic
486C22×C32C22×D411yescharacteristic
487C22×C32C2×#4111yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—416no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C32×C4—22no—
508C32×C4—22no—
509C32×C4—41no—
510C32×C4—41no—
511C32×C4—41no—
512C3×Dic3—22no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—41no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C25—31no—
519C22×D4—31no—
520C22×D4—31no—
521C22×D4C2×C3×D311yescharacteristic
522C23×C4—31no—
523C23×C4C2×C3×D311yescharacteristic
524C23×C4C2×C3×D311yescharacteristic, complemented
525#123—64no—
526#120—64no—
527C4×D4—24no—
528C2×C4⋊C4—31no—
529C2×C4⋊C4—31no—
530C2×C4⋊C4—31no—
531C2×C4⋊C4—31no—
532C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—31no—
540C2×C22⋊C4—31no—
541C2×C22⋊C4—31no—
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—64no—
548C2×C22⋊C4C2×C3×D311yescharacteristic
549C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
550C2×C42C2×C3×D311yescharacteristic, complemented
551#95—31no—
552#95—31no—
553#95—31no—
554#95—31no—
555#95—31no—
556#95—31no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—22no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—32no—
585C23×C3—32no—
586C23×C3—41no—
587C23×C3—41no—
588C23×C3—41no—
589C23×C3—41no—
590C23×C3—41no—
591C23×C3—41no—
592C23×C3—41no—
593C23×C3—41no—
594C23×C3—68no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—124no—
608C23×C3—124no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—124no—
612C23×C3—124no—
613C23×C3#23512yes—
614C23×C3#23512yes—
615C23×C3C2×#6712yes—
616C23×C3C2×#6712yes—
617C23×C3C2×C3×D412yes—
618C23×C3C2×C3×D412yes—
619C23×C3C3×#4112yes—
620C23×C3C3×#4112yes—
621C23×C3C23×D311yescharacteristic
622C23×C3C24×C311yescharacteristic
623C22×D3—28no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—44no—
637C22×D3—44no—
638C22×D3—44no—
639C22×D3—44no—
640C22×D3—44no—
641C22×D3—44no—
642C22×D3C2×C3×D412yes—
643C22×D3C3×#4112yes—
644C3×D4—216no—
645C3×D4—28no—
646C3×D4—28no—
647C3×D4—124no—
648C3×D4—124no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—32no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—44no—
692C2×C3×C4—44no—
693C2×C3×C4—44no—
694C2×C3×C4—44no—
695C2×C3×C4—48no—
696C2×C3×C4—48no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—124no—
715C2×C3×C4D3×D412yes—
716C2×C3×C4C2×#6712yes—
717C2×C3×C4C2×C3×D412yes—
718C2×C3×C4C2×C3×D412yes—
719#67—44no—
720#67—44no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—44no—
739C2×Dic3C2×C3×D412yes—
740C2×C32—24no—
741C2×C32—42no—
742C2×C32C2×#12311yescharacteristic
743C2×C32#52511yescharacteristic
744C2×C32#53811yescharacteristic
745C2×C32D4211yescharacteristic
746C2×C32#54611yescharacteristic
747C2×C32#54611yescharacteristic
748C2×C32#55111yescharacteristic
749C3×D3—42no—
750C3×D3—42no—
751C24—31no—
752C24—31no—
753C24—62no—
754C24—62no—
755C24—62no—
756C24—62no—
757C24—62no—
758C24—121no—
759C24—121no—
760C24C22×C3×D311yescharacteristic
761C24C22×C3×D311yescharacteristic
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—62no—
765C2×D4—62no—
766C2×D4—62no—
767C2×D4—62no—
768C2×D4—121no—
769C2×D4—121no—
770C2×D4C3×#6714yes—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—31no—
776C22×C4—31no—
777C22×C4—31no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—121no—
786C22×C4C22×C3×D311yescharacteristic
787C22×C4C22×C3×D311yescharacteristic
788C22×C4C22×C3×D311yescharacteristic
789C22×C4C22×C3×D311yescharacteristic
790C22×C4C22×C3×D311yescharacteristic
791C4⋊C4—22no—
792C4⋊C4—62no—
793C4⋊C4—62no—
794C4⋊C4—121no—
795C4⋊C4—121no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—34no—
799C22⋊C4—62no—
800C22⋊C4—62no—
801C22⋊C4—62no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—62no—
805C22⋊C4—62no—
806C22⋊C4—62no—
807C22⋊C4—62no—
808C22⋊C4—62no—
809C22⋊C4—121no—
810C22⋊C4—121no—
811C22⋊C4—121no—
812C42—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—24no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—24no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—41no—
859C22×C3—41no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—1216no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3#92914yescomplemented
876C22×C3C3×#12314yescomplemented
877C22×C3C2×#23511yescharacteristic
878C22×C3C2×#23511yescharacteristic
879C22×C3C2×D3×D411yescharacteristic
880C22×C3#100411yescharacteristic
881C22×C3D3×#4111yescharacteristic
882C22×C3#100911yescharacteristic
883C22×C3C22×#6711yescharacteristic
884C22×C3C22×C3×D411yescharacteristic
885C22×C3C22×C3×D411yescharacteristic
886C22×C3C2×C3×#4111yescharacteristic
887C22×C3C2×C3×#4111yescharacteristic
888C22×C3C2×C3×#4111yescharacteristic
889C22×C3C3×H(5,𝔽2)11yescharacteristic
890C22×C3C3×H(5,𝔽2)11yescharacteristic
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—22no—
897C2×D3—416no—
898C2×D3—41no—
899C2×D3—41no—
900C2×D3—41no—
901C2×D3—41no—
902C2×D3—41no—
903C2×D3—41no—
904C2×D3—41no—
905C2×D3—41no—
906C3×C4—24no—
907C3×C4—24no—
908C3×C4—22no—
909C3×C4—22no—
910C3×C4—22no—
911C3×C4—22no—
912C3×C4—42no—
913C3×C4—42no—
914C3×C4—42no—
915C3×C4—41no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—62no—
922C3×C4—121no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927Dic3—22no—
928Dic3—41no—
929Dic3—41no—
930Dic3—41no—
931Dic3—41no—
932Dic3—41no—
933C32#241811yescharacteristic, complemented, Sylow
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—32no—
945C23—32no—
946C23—68no—
947C23—61no—
948C23—61no—
949C23—61no—
950C23—61no—
951C23—61no—
952C23—61no—
953C23—61no—
954C23—61no—
955C23—61no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—124no—
960C23—124no—
961C23—124no—
962C23—124no—
963C23—124no—
964C23—124no—
965C23C3×#23512yes—
966C23C3×#23512yes—
967C23C2×C3×#6712yes—
968C23C2×C3×#6712yes—
969C23C23×C3×D311yescharacteristic
970D4—28no—
971D4—124no—
972D4—124no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—32no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—61no—
990C2×C4—61no—
991C2×C4—61no—
992C2×C4—61no—
993C2×C4—61no—
994C2×C4—61no—
995C2×C4—61no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—61no—
999C2×C4—61no—
1000C2×C4—61no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—124no—
1007C2×C4C3×D3×D412yes—
1008C2×C4C2×C3×#6712yes—
1009C2×C3—24no—
1010C2×C3—24no—
1011C2×C3—21no—
1012C2×C3—21no—
1013C2×C3—21no—
1014C2×C3—21no—
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—44no—
1019C2×C3—44no—
1020C2×C3—42no—
1021C2×C3—42no—
1022C2×C3—122no—
1023C2×C3—122no—
1024C2×C3#554711yescharacteristic
1025C2×C3#555011yescharacteristic
1026C2×C3#555611yescharacteristic
1027C2×C3#556011yescharacteristic
1028C2×C3C2×#92911yescharacteristic
1029C2×C3D4×#6711yescharacteristic
1030C2×C3#582911yescharacteristic
1031C2×C3C2×C3×#12311yescharacteristic
1032C2×C3C3×#52511yescharacteristic
1033C2×C3C3×#53811yescharacteristic
1034C2×C3C3×D4211yescharacteristic
1035C2×C3C3×#54611yescharacteristic
1036C2×C3C3×#54611yescharacteristic
1037C2×C3C3×#55111yescharacteristic
1038D3—42no—
1039D3—42no—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—41no—
1053C22—62no—
1054C22—62no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—1216no—
1060C22—121no—
1061C22—121no—
1062C22—121no—
1063C22—121no—
1064C22—121no—
1065C22—121no—
1066C22—121no—
1067C22—121no—
1068C22C3×#92914yescomplemented
1069C22C2×C3×#23511yescharacteristic
1070C22C2×C3×#23511yescharacteristic
1071C22C2×C3×D3×D411yescharacteristic
1072C22C3×#100411yescharacteristic
1073C22C3×D3×#4111yescharacteristic
1074C22C3×#100911yescharacteristic
1075C22C22×C3×#6711yescharacteristic
1076C4—22no—
1077C4—22no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—62no—
1082C4—121no—
1083C4—121no—
1084C4—121no—
1085C4—121no—
1086C4—121no—
1087C3—21no—
1088C3#8240411yescharacteristic, direct product factor
1089C3C3×#241811yescharacteristic, complemented
1090C2—24no—
1091C2—42no—
1092C2—122no—
1093C2—122no—
1094C2C3×#554711yescharacteristic
1095C2C3×#555011yescharacteristic
1096C2C3×#555611yescharacteristic
1097C2C3×#556011yescharacteristic
1098C2C2×C3×#92911yescharacteristic
1099C2C3×D4×#6711yescharacteristic
1100C2C3×#582911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2418
LCSG ▷ C23×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×#929C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C3×#5220C2semidirect
6. C3×#5213C2semidirect
7. C3×#5210C2semidirect
8. C3×#4993C2semidirect
9. C3×#4992C2semidirect
10. C3×#4959C2semidirect
11. C3×#4959C2semidirect
12. C3×#4955C2semidirect
13. C3×#4942C2semidirect
14. C3×#4940C2semidirect
15. C3×#4940C2semidirect
17. #82404C3direct (N × H)
21. C23×C32×C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×C32×C42C22semidirect
32. C2×C3×#217C22semidirect
33. C2×C3×#217C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
60. C2×C3×C4×D4D3semidirect
61. C2×C3×C4×D4C2×C3semidirect
64. C2×#929C2×C3semidirect
65. C22×(C2×D3)⋊C4C2×C3semidirect
77. #5220C2×C3semidirect
78. #5213C2×C3semidirect
79. #5210C2×C3semidirect
80. #4993C2×C3semidirect
81. #4992C2×C3semidirect
82. #4959C2×C3semidirect
83. #4959C2×C3semidirect
84. #4955C2×C3semidirect
85. #4942C2×C3semidirect
86. #4940C2×C3semidirect
87. #4940C2×C3semidirect
145. C3×(C2×D3)⋊C4D4semidirect
162. C23×C3×C4C2×D3semidirect
164. C23×C3×C4C22×C3semidirect
178. C2×C3×C4⋊C4C2×D3semidirect
179. C2×C3×C4⋊C4C22×C3semidirect
198. C2×C3×C22⋊C4C2×D3semidirect
200. C2×C3×C22⋊C4C22×C3semidirect
202. C2×C3×C42C2×D3semidirect
203. C2×C3×C42C22×C3semidirect
206. C2×#217C22×C3semidirect
207. C2×#217C22×C3semidirect
221. C2×Dic3⋊C4C22×C3semidirect
222. C2×Dic3⋊C4C22×C3semidirect
223. C2×Dic3⋊C4C22×C3semidirect
224. C2×Dic3⋊C4C22×C3semidirect
231. C3⋊#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
236. C3⋊#95C22×C3semidirect
314. C2×C4×D4C3×D3semidirect
466. (C2×D3)⋊C4C3×D4semidirect
484. C22×C32#123semidirect
524. C23×C4C2×C3×D3semidirect
532. C2×C4⋊C4C2×C3×D3semidirect
549. C2×C22⋊C4C2×C3×D3semidirect
550. C2×C42C2×C3×D3semidirect
875. C22×C3#929semidirect
876. C22×C3C3×#123semidirect
933. C32#2418semidirect
1068. C22C3×#929semidirect
1088. C3#82404direct (N × H)
1089. C3C3×#2418semidirect

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×#9372
C2×C3×#9292
C22×C3×(C2×D3)⋊C42
C3×#52202
C3×#52132
C3×#52102
C3×#49932
C3×#49922
C3×#49592
C3×#49552
C3×#49422
C3×#49402
C3×#24183
#824043