Finite Group Databasebeta

← C3×#74603 #11810303

Subgroups — C3×#74603 #11810303

Order 1152.

1717 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic, complemented
2C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic
5C32×#385C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8C3×#4990C211yesmaximal, characteristic, complemented
9C3×#4958C211yesmaximal, characteristic, complemented
10C3×#4955C211yesmaximal, characteristic, complemented
11C3×#4942C211yesmaximal, characteristic, complemented
12C3×#4675C211yesmaximal, characteristic, complemented
13C3×#4672C211yesmaximal, characteristic, complemented
14C3×#4669C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#74603C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C3×C4×#67—24no—
31C2×C3×(C2×D3)⋊C4—24no—
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×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×C4×Dic3C2211yescharacteristic, complemented
49C3×#894—24no—
50C3×#882—24no—
51C32×#95C2211yescharacteristic, complemented
52C32×#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—31no—
60C22×C3×C22⋊C4—31no—
61C2×C4×#67C2×C311yescharacteristic, complemented
62C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
63C2×#894C2×C311yescharacteristic, complemented
64C2×#882C2×C311yescharacteristic
65C3×#399—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#394—31no—
69C3×#388—31no—
70C3×#388—31no—
71C3×#386—31no—
72C3×#386—31no—
73C3×#385—21no—
74C3×#385D311yescharacteristic, complemented
75C3×#385C2×C311yescharacteristic, complemented
76C3×#380—31no—
77C3×#379—31no—
78#4993C2×C311yescharacteristic, complemented
79#4991C2×C311yescharacteristic, complemented
80#4990C2×C311yescharacteristic, complemented
81#4958C2×C311yescharacteristic, complemented
82#4955C2×C311yescharacteristic, complemented
83#4942C2×C311yescharacteristic, complemented
84#4675C2×C311yescharacteristic, complemented
85#4672C2×C311yescharacteristic, complemented
86#4669C2×C311yescharacteristic, complemented
87#4665C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—41no—
95C23×C3×D3—41no—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C23×C3×D3C2311yescharacteristic
99C22×C32×C4—22no—
100C22×C32×C4—22no—
101C22×C32×C4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×C3×#67—22no—
109C2×C3×#67—22no—
110C2×C3×#67D414yes—
111C22×C3×Dic3—22no—
112C22×C3×Dic3—22no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×D12—22no—
120C2×C3×D12—22no—
121C2×C3×D12—22no—
122C2×C3×D12—22no—
123C2×C3×D12—41no—
124C2×C3×D12—41no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3—41no—
128C32×C4⋊C4—22no—
129C32×C4⋊C4—41no—
130C32×C22⋊C4—22no—
131C32×C22⋊C4—22no—
132C3×#217—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
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—41no—
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×C4×Dic3—22no—
150#2418—31noSylow
151C25×C3—31no—
152C24×D3C22×C311yescharacteristic
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C23×C3×C4—21no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C23×C3×C4C2×D311yescharacteristic
160C23×C3×C4C22×C311yescharacteristic
161C22×#67C22×C311yescharacteristic
162C23×Dic3C22×C311yescharacteristic
163C22×D12C22×C311yescharacteristic
164C22×D12C22×C311yescharacteristic
165C22×C4×D3C22×C311yescharacteristic, complemented
166C3×#123—64no—
167C3×#120—64no—
168C3×C4×D4—64no—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—21no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
176C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
177C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—21no—
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⋊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—64no—
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C22×C311yescharacteristic
198C2×C3×C22⋊C4C22×C311yescharacteristic
199C2×C3×C42—31no—
200C2×#217C22×C311yescharacteristic
201C4×#67—24no—
202C2×(C2×D3)⋊C4—24no—
203C2×(C2×D3)⋊C4C22×C311yescharacteristic
204C2×(C2×D3)⋊C4C22×C311yescharacteristic
205C2×(C2×D3)⋊C4C22×C311yescharacteristic
206C2×(C2×D3)⋊C4C22×C311yescharacteristic
207C2×(C2×D3)⋊C4C22×C311yescharacteristic
208C2×(C2×D3)⋊C4C22×C311yescharacteristic
209C2×(C2×D3)⋊C4C22×C311yescharacteristic
210C2×(C2×D3)⋊C4C22×C311yescharacteristic
211C2×(C2×D3)⋊C4C22×C311yescharacteristic
212C2×(C2×D3)⋊C4C22×C311yescharacteristic
213C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
214C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
215C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
216C2×Dic3⋊C4C22×C311yescharacteristic, complemented
217C2×Dic3⋊C4C22×C311yescharacteristic, complemented
218C2×Dic3⋊C4C22×C311yescharacteristic, complemented
219C2×C4×Dic3C22×C311yescharacteristic, complemented
220#894—24no—
221#882—24no—
222C3×#95—21no—
223C3×#95—21no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95—31no—
227C3×#95—31no—
228C3×#95C2×D311yescharacteristic, complemented
229C3×#95C2×D311yescharacteristic, complemented
230C3×#95C22×C311yescharacteristic, complemented
231C3×#95C22×C311yescharacteristic, complemented
232C3⋊#95C22×C311yescharacteristic, complemented
233C3⋊#95C22×C311yescharacteristic, complemented
234C3⋊#95C22×C311yescharacteristic, complemented
235C3⋊#95C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C2×D412yes—
241C23×C32#4112yes—
242C23×C32#4112yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—28no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
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—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3—44no—
268C22×C3×D3—44no—
269C22×C3×D3C2×D412yes—
270C22×C3×D3C2×D412yes—
271C22×C3×D3#4112yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
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—21no—
288C2×C32×C4—21no—
289C2×C32×C4—44no—
290C2×C32×C4C2×D412yes—
291C3×#67—28no—
292C2×C3×Dic3—21no—
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—44no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C3×D12—44no—
309C3×D12—44no—
310C3×C4×D3—44no—
311C2×#123—31no—
312C2×#120—31no—
313C2×C4×D4—31no—
314C22×C22⋊C4—31no—
315#399—31no—
316#397—31no—
317#394—31no—
318#394—31no—
319#388—31no—
320#388—31no—
321#386—31no—
322#386—31no—
323#385C3×D311yescharacteristic, complemented
324#380—31no—
325#379—31no—
326C24×C3—21no—
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—62no—
331C24×C3—62no—
332C24×C3—62no—
333C24×C3—62no—
334C24×C3—62no—
335C24×C3—121no—
336C24×C3—121no—
337C24×C3C22×D311yescharacteristic
338C24×C3C23×C311yescharacteristic
339C23×D3—22no—
340C23×D3—22no—
341C23×D3—22no—
342C23×D3—22no—
343C23×D3—22no—
344C23×D3—41no—
345C23×D3—41no—
346C23×D3C23×C311yescharacteristic
347C23×D3C23×C311yescharacteristic
348C23×D3C23×C311yescharacteristic
349C2×C3×D4—34no—
350C2×C3×D4—62no—
351C2×C3×D4—62no—
352C2×C3×D4—62no—
353C2×C3×D4—62no—
354C2×C3×D4—62no—
355C2×C3×D4—62no—
356C2×C3×D4—121no—
357C2×C3×D4—121no—
358C22×C3×C4—22no—
359C22×C3×C4—22no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—42no—
374C22×C3×C4—42no—
375C22×C3×C4—41no—
376C22×C3×C4—41no—
377C22×C3×C4—42no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—62no—
381C22×C3×C4—62no—
382C22×C3×C4—121no—
383C22×C3×C4—121no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C23×C311yescharacteristic
391C22×C3×C4C23×C311yescharacteristic
392C22×C3×C4C23×C311yescharacteristic
393C22×C3×C4C23×C311yescharacteristic
394C22×C3×C4C23×C311yescharacteristic
395C22×C3×C4C23×C311yescharacteristic
396C2×#67—22no—
397C2×#67—22no—
398C2×#67C3×D414yes—
399C22×Dic3—22no—
400C22×Dic3—22no—
401C22×Dic3—41no—
402C22×Dic3C23×C311yescharacteristic
403C22×Dic3C23×C311yescharacteristic
404C22×Dic3C23×C311yescharacteristic
405C22×Dic3C23×C311yescharacteristic
406C22×Dic3C23×C311yescharacteristic
407C2×D12—22no—
408C2×D12—22no—
409C2×D12—22no—
410C2×D12—22no—
411C2×D12—41no—
412C2×D12—41no—
413C2×C4×D3—22no—
414C2×C4×D3—22no—
415C2×C4×D3—41no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—22no—
418C3×C4⋊C4—42no—
419C3×C4⋊C4—41no—
420C3×C4⋊C4—41no—
421C3×C4⋊C4—42no—
422C3×C4⋊C4—62no—
423C3×C4⋊C4—62no—
424C3×C4⋊C4—121no—
425C3×C22⋊C4—24no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—42no—
432C3×C22⋊C4—62no—
433C3×C22⋊C4—62no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—62no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—62no—
438C3×C22⋊C4—62no—
439C3×C22⋊C4—62no—
440C3×C22⋊C4—62no—
441C3×C22⋊C4—62no—
442C3×C22⋊C4—121no—
443C3×C22⋊C4—121no—
444C3×C22⋊C4—121no—
445C3×C42—62no—
446#217—22no—
447(C2×D3)⋊C4—22no—
448(C2×D3)⋊C4—22no—
449(C2×D3)⋊C4—22no—
450(C2×D3)⋊C4—22no—
451(C2×D3)⋊C4—22no—
452(C2×D3)⋊C4—22no—
453(C2×D3)⋊C4—22no—
454(C2×D3)⋊C4—22no—
455(C2×D3)⋊C4—22no—
456(C2×D3)⋊C4—41no—
457(C2×D3)⋊C4—41no—
458(C2×D3)⋊C4—41no—
459(C2×D3)⋊C4C3×D414yescomplemented
460Dic3⋊C4—22no—
461Dic3⋊C4—22no—
462Dic3⋊C4—41no—
463C4×Dic3—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32#12314yescomplemented
471C22×C32C22×D411yescharacteristic
472C22×C32C22×D411yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32C2×#4111yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—416no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C2×C3×D3—41no—
499C2×C3×D3—41no—
500C32×C4—22no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C25—31no—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—31no—
515C23×C4—31no—
516C23×C4—31no—
517C23×C4C2×C3×D311yescharacteristic
518#123—64no—
519#120—64no—
520C4×D4—64no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
525C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
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—64no—
541C2×C22⋊C4C2×C3×D311yescharacteristic
542C2×C22⋊C4C2×C3×D311yescharacteristic
543C2×C42—31no—
544#95—31no—
545#95—31no—
546#95—31no—
547#95—31no—
548#95C2×C3×D311yescharacteristic, complemented
549#95C2×C3×D311yescharacteristic, complemented
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—21no—
558C23×C3—21no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—68no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—124no—
589C23×C3—124no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3#23512yes—
595C23×C3D3×D412yes—
596C23×C3#23912yes—
597C23×C3C2×C3×D412yes—
598C23×C3C3×#4112yes—
599C23×C3C3×#4112yes—
600C23×C3C23×D311yescharacteristic
601C23×C3C24×C311yescharacteristic
602C22×D3—28no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3—44no—
624C22×D3—44no—
625C22×D3—44no—
626C22×D3—44no—
627C22×D3C2×C3×D412yes—
628C22×D3C2×C3×D412yes—
629C22×D3C3×#4112yes—
630C3×D4—68no—
631C3×D4—124no—
632C3×D4—124no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
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—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
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—22no—
671C2×C3×C4—32no—
672C2×C3×C4—32no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—44no—
688C2×C3×C4—44no—
689C2×C3×C4—48no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
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—124no—
704C2×C3×C4—124no—
705C2×C3×C4D3×D412yes—
706C2×C3×C4C2×C3×D412yes—
707#67—28no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
721C2×Dic3—44no—
722C2×Dic3C2×C3×D412yes—
723C2×Dic3C2×C3×D412yes—
724D12—44no—
725D12—44no—
726C4×D3—44no—
727C2×C32—24no—
728C2×C32C2×#12311yescharacteristic
729C2×C32#52511yescharacteristic
730C2×C32#53811yescharacteristic
731C2×C32D4211yescharacteristic
732C2×C32#54611yescharacteristic
733C2×C32#54611yescharacteristic
734C2×C32#55111yescharacteristic
735C3×D3—42no—
736C3×D3—42no—
737C3×D3—42no—
738C24—31no—
739C24—31no—
740C24—31no—
741C24—62no—
742C24—62no—
743C24—62no—
744C24—62no—
745C24—62no—
746C24—121no—
747C24—121no—
748C24C22×C3×D311yescharacteristic
749C2×D4—34no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4—62no—
754C2×D4—62no—
755C2×D4—62no—
756C2×D4—121no—
757C2×D4—121no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—41no—
766C22×C4—62no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—62no—
770C22×C4—121no—
771C22×C4—121no—
772C22×C4C22×C3×D311yescharacteristic
773C22×C4C22×C3×D311yescharacteristic
774C22×C4C22×C3×D311yescharacteristic
775C22×C4C22×C3×D311yescharacteristic
776C22×C4C22×C3×D311yescharacteristic
777C22×C4C22×C3×D311yescharacteristic
778C4⋊C4—22no—
779C4⋊C4—41no—
780C4⋊C4—62no—
781C4⋊C4—62no—
782C4⋊C4—121no—
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—34no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—62no—
794C22⋊C4—62no—
795C22⋊C4—62no—
796C22⋊C4—121no—
797C22⋊C4—121no—
798C22⋊C4—121no—
799C42—62no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—24no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—42no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—1216no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—121no—
848C22×C3#89414yescomplemented
849C22×C3C3×#12314yescomplemented
850C22×C3C2×#23511yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C22×C3C2×D3×D411yescharacteristic
853C22×C3#100411yescharacteristic
854C22×C3C2×#23911yescharacteristic
855C22×C3D3×#4111yescharacteristic
856C22×C3#100911yescharacteristic
857C22×C3C22×C3×D411yescharacteristic
858C22×C3C22×C3×D411yescharacteristic
859C22×C3C2×C3×#4111yescharacteristic
860C22×C3C2×C3×#4111yescharacteristic
861C22×C3C2×C3×#4111yescharacteristic
862C22×C3C3×H(5,𝔽2)11yescharacteristic
863C22×C3C3×H(5,𝔽2)11yescharacteristic
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—416no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—41no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—41no—
901C3×C4—41no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—81no—
905C3×C4—81no—
906C3×C4—121no—
907C3×C4—121no—
908C3×C4—121no—
909Dic3—22no—
910Dic3—22no—
911Dic3—41no—
912Dic3—41no—
913Dic3—41no—
914C32#241811yescharacteristic, complemented, Sylow
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—68no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23—124no—
947C23C3×#23512yes—
948C23C3×D3×D412yes—
949C23C3×#23912yes—
950C23C23×C3×D311yescharacteristic
951D4—68no—
952D4—124no—
953D4—124no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—32no—
972C2×C4—32no—
973C2×C4—44no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—61no—
987C2×C4—124no—
988C2×C4—124no—
989C2×C4C3×D3×D412yes—
990C2×C3—24no—
991C2×C3—24no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—44no—
1000C2×C3—122no—
1001C2×C3—122no—
1002C2×C3—122no—
1003C2×C3C2×#89411yescharacteristic
1004C2×C3#554711yescharacteristic
1005C2×C3#556011yescharacteristic
1006C2×C3#559011yescharacteristic
1007C2×C3#563011yescharacteristic
1008C2×C3#563711yescharacteristic
1009C2×C3#565411yescharacteristic
1010C2×C3C2×C3×#12311yescharacteristic
1011C2×C3C3×#52511yescharacteristic
1012C2×C3C3×#53811yescharacteristic
1013C2×C3C3×D4211yescharacteristic
1014C2×C3C3×#54611yescharacteristic
1015C2×C3C3×#54611yescharacteristic
1016C2×C3C3×#55111yescharacteristic
1017D3—42no—
1018D3—42no—
1019D3—42no—
1020C22—22no—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—1216no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22—121no—
1047C22—121no—
1048C22C3×#89414yescomplemented
1049C22C2×C3×#23511yescharacteristic
1050C22C2×C3×D3×D411yescharacteristic
1051C22C2×C3×D3×D411yescharacteristic
1052C22C3×#100411yescharacteristic
1053C22C2×C3×#23911yescharacteristic
1054C22C3×D3×#4111yescharacteristic
1055C22C3×#100911yescharacteristic
1056C4—22no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—62no—
1063C4—62no—
1064C4—121no—
1065C4—121no—
1066C4—121no—
1067C3—21no—
1068C3#7460311yescharacteristic, direct product factor
1069C3C3×#241811yescharacteristic, complemented
1070C2—24no—
1071C2—122no—
1072C2—122no—
1073C2—122no—
1074C2C2×C3×#89411yescharacteristic
1075C2C3×#554711yescharacteristic
1076C2C3×#556011yescharacteristic
1077C2C3×#559011yescharacteristic
1078C2C3×#563011yescharacteristic
1079C2C3×#563711yescharacteristic
1080C2C3×#565411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC3×#385D3
hypocenterC3C3×#2418
LCSG ▷ C23×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. C22×C3×(C2×D3)⋊C4C2semidirect
3. C2×C3×#894C2semidirect
5. C32×#385C2semidirect
6. C3×#4993C2semidirect
7. C3×#4991C2semidirect
8. C3×#4990C2semidirect
9. C3×#4958C2semidirect
10. C3×#4955C2semidirect
11. C3×#4942C2semidirect
12. C3×#4675C2semidirect
13. C3×#4672C2semidirect
14. C3×#4669C2semidirect
15. C3×#4665C2semidirect
17. #74603C3direct (N × H)
24. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×(C2×D3)⋊C4C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×C4×Dic3C22semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
61. C2×C4×#67C2×C3semidirect
62. C22×(C2×D3)⋊C4C2×C3semidirect
63. C2×#894C2×C3semidirect
74. C3×#385D3semidirect
75. C3×#385C2×C3semidirect
78. #4993C2×C3semidirect
79. #4991C2×C3semidirect
80. #4990C2×C3semidirect
81. #4958C2×C3semidirect
82. #4955C2×C3semidirect
83. #4942C2×C3semidirect
84. #4675C2×C3semidirect
85. #4672C2×C3semidirect
86. #4669C2×C3semidirect
87. #4665C2×C3semidirect
145. C3×(C2×D3)⋊C4D4semidirect
165. C22×C4×D3C22×C3semidirect
174. C2×C3×C4⋊C4C2×D3semidirect
175. C2×C3×C4⋊C4C2×D3semidirect
176. C2×C3×C4⋊C4C22×C3semidirect
177. C2×C3×C4⋊C4C22×C3semidirect
213. C2×(C2×D3)⋊C4C22×C3semidirect
214. C2×(C2×D3)⋊C4C22×C3semidirect
215. C2×(C2×D3)⋊C4C22×C3semidirect
216. C2×Dic3⋊C4C22×C3semidirect
217. C2×Dic3⋊C4C22×C3semidirect
218. C2×Dic3⋊C4C22×C3semidirect
219. C2×C4×Dic3C22×C3semidirect
228. C3×#95C2×D3semidirect
229. C3×#95C2×D3semidirect
230. C3×#95C22×C3semidirect
231. C3×#95C22×C3semidirect
232. C3⋊#95C22×C3semidirect
233. C3⋊#95C22×C3semidirect
234. C3⋊#95C22×C3semidirect
235. C3⋊#95C22×C3semidirect
323. #385C3×D3semidirect
459. (C2×D3)⋊C4C3×D4semidirect
470. C22×C32#123semidirect
524. C2×C4⋊C4C2×C3×D3semidirect
525. C2×C4⋊C4C2×C3×D3semidirect
548. #95C2×C3×D3semidirect
549. #95C2×C3×D3semidirect
848. C22×C3#894semidirect
849. C22×C3C3×#123semidirect
914. C32#2418semidirect
1048. C22C3×#894semidirect
1068. C3#74603direct (N × H)
1069. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×(C2×D3)⋊C42
C2×C3×#8942
C2×C3×#8822
C32×#3852
C3×#49932
C3×#49912
C3×#49902
C3×#49582
C3×#49552
C3×#49422
C3×#46752
C3×#46722
C3×#46692
C3×#46652
C3×#24183
#746033