Finite Group Databasebeta

← C3×#75844 #11810312

Subgroups — C3×#75844 #11810312

Order 1152.

1695 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#883C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic
3C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C32×#388C211yesmaximal, characteristic, complemented
6C3×#4991C211yesmaximal, characteristic, complemented
7C3×#4987C211yesmaximal, characteristic, complemented
8C3×#4961C211yesmaximal, characteristic, complemented
9C3×#4955C211yesmaximal, characteristic, complemented
10C3×#4953C211yesmaximal, characteristic, complemented
11C3×#4940C211yesmaximal, characteristic, complemented
12C3×#4677C211yesmaximal, characteristic, complemented
13C3×#4668C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2418—31nomaximal
17#75844C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C42C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
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, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#883—24no—
48C3×#882—24no—
49C3×D3×C22⋊C4—24no—
50C3×C4×D12—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×#883C2×C311yescharacteristic, complemented
62C2×#882C2×C311yescharacteristic
63C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
64C2×C4×D12C2×C311yescharacteristic, complemented
65C3×#399—31no—
66C3×#397—31no—
67C3×#394—31no—
68C3×#394—31no—
69C3×#388—21no—
70C3×#388—31no—
71C3×#388D311yescharacteristic, complemented
72C3×#388C2×C311yescharacteristic, complemented
73C3×#386—31no—
74C3×#386—31no—
75C3×#385—31no—
76C3×#380—31no—
77C3×#379—31no—
78#4991C2×C311yescharacteristic, complemented
79#4987C2×C311yescharacteristic, complemented
80#4961C2×C311yescharacteristic, complemented
81#4955C2×C311yescharacteristic, complemented
82#4953C2×C311yescharacteristic, complemented
83#4940C2×C311yescharacteristic, complemented
84#4677C2×C311yescharacteristic, complemented
85#4668C2×C311yescharacteristic, complemented
86#4665C2×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×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C2×C3×#67—22no—
106C2×C3×#67—22no—
107C2×C3×#67—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—41no—
118C2×C3×D12D414yes—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×C3×C4×D3—22no—
125C2×C3×C4×D3—41no—
126C2×C3×C4×D3—41no—
127C2×C3×C4×D3—41no—
128C32×C4⋊C4—41no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—41no—
131C32×C22⋊C4D414yescomplemented
132C32×C42—22no—
133C3×#217—22no—
134C3×#217—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—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—41no—
145C3×(C2×D3)⋊C4—41no—
146C3×C4⋊Dic3—22no—
147C3×C4⋊Dic3—22no—
148C3×C4⋊Dic3—41no—
149C3×Dic3⋊C4—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—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C22×#67C22×C311yescharacteristic
160C22×D12C22×C311yescharacteristic
161C22×D12C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C22×C4×D3C22×C311yescharacteristic
164C22×C4×D3C22×C311yescharacteristic, complemented
165C3×#123—64no—
166C3×#120—64no—
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, complemented
174C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—21no—
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⋊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—64no—
192C2×C3×C22⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C22×C311yescharacteristic
196C2×C3×C22⋊C4C22×C311yescharacteristic
197C2×C3×C22⋊C4C22×C311yescharacteristic
198C2×C3×C42—21no—
199C2×C3×C42C2×D311yescharacteristic, complemented
200C2×C3×C42C22×C311yescharacteristic, complemented
201C2×#217C22×C311yescharacteristic
202C2×#217C22×C311yescharacteristic
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, complemented
212C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
213C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
214C2×C4⋊Dic3C22×C311yescharacteristic, complemented
215C2×C4⋊Dic3C22×C311yescharacteristic, complemented
216C2×C4⋊Dic3C22×C311yescharacteristic, complemented
217C2×Dic3⋊C4C22×C311yescharacteristic, complemented
218#883—24no—
219#882—24no—
220D3×C22⋊C4—24no—
221C4×D12—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×C32—21no—
241C23×C32—21no—
242C23×C32C2×D412yes—
243C23×C32C2411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—28no—
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—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3—44no—
267C22×C3×D3C2×D412yes—
268C22×C3×D3C2×D412yes—
269C22×C3×D3#4112yes—
270C22×C3×D3#4112yes—
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×C4C2×D412yes—
288C2×C32×C4C2×D412yes—
289C2×C32×C4C2×D412yes—
290C3×#67—44no—
291C2×C3×Dic3—21no—
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—21no—
306C3×D12—28no—
307C3×D12—44no—
308C3×C4×D3—44no—
309C3×C4×D3—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#388C3×D311yescharacteristic, complemented
321#386—31no—
322#386—31no—
323#385—31no—
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—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—62no—
370C22×C3×C4—62no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4—121no—
376C22×C3×C4—121no—
377C22×C3×C4—121no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C23×C311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C22×C3×C4C23×C311yescharacteristic
388C22×C3×C4C23×C311yescharacteristic
389C22×C3×C4C23×C311yescharacteristic
390C2×#67—22no—
391C2×#67—22no—
392C2×#67—41no—
393C22×Dic3C23×C311yescharacteristic
394C22×Dic3C23×C311yescharacteristic
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C2×D12—22no—
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—41no—
403C2×D12C3×D414yes—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—22no—
407C2×C4×D3—22no—
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—41no—
411C2×C4×D3—41no—
412C2×C4×D3—41no—
413C3×C4⋊C4—41no—
414C3×C4⋊C4—41no—
415C3×C4⋊C4—42no—
416C3×C4⋊C4—62no—
417C3×C4⋊C4—62no—
418C3×C4⋊C4—62no—
419C3×C4⋊C4—121no—
420C3×C22⋊C4—22no—
421C3×C22⋊C4—22no—
422C3×C22⋊C4—24no—
423C3×C22⋊C4—42no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—41no—
426C3×C22⋊C4—42no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—62no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
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—121no—
439C3×C22⋊C4—121no—
440C3×C22⋊C4D1214yescomplemented
441C3×C22⋊C4C3×D414yescomplemented
442C3×C42—22no—
443C3×C42—22no—
444C3×C42—42no—
445#217—22no—
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—
458C4⋊Dic3—22no—
459C4⋊Dic3—22no—
460C4⋊Dic3—41no—
461Dic3⋊C4—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C22×C32C22×D411yescharacteristic
471C22×C32C2×#4111yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32C2×#4111yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C2×C3×D3—22no—
477C2×C3×D3—22no—
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—22no—
488C2×C3×D3—416no—
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#12314yescomplemented
498C32×C4—22no—
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—41no—
502C32×C4—41no—
503C32×C4—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C25—31no—
510C22×D4—31no—
511C22×D4—31no—
512C22×D4—31no—
513C23×C4—31no—
514C23×C4—31no—
515C23×C4—31no—
516#123—64no—
517#120—64no—
518C4×D4—64no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
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—64no—
538C2×C22⋊C4C2×C3×D311yescharacteristic
539C2×C22⋊C4C2×C3×D311yescharacteristic
540C2×C22⋊C4C2×C3×D311yescharacteristic
541C2×C42C2×C3×D311yescharacteristic, complemented
542#95—31no—
543#95—31no—
544#95—31no—
545#95—31no—
546#95C2×C3×D311yescharacteristic, complemented
547#95C2×C3×D311yescharacteristic, complemented
548C23×C3—21no—
549C23×C3—21no—
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—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—41no—
573C23×C3—68no—
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—61no—
589C23×C3—61no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3—124no—
593C23×C3—124no—
594C23×C3—124no—
595C23×C3—124no—
596C23×C3C2×D1212yes—
597C23×C3C2×C3×D412yes—
598C23×C3C23×D311yescharacteristic
599C23×C3C24×C311yescharacteristic
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—28no—
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—44no—
618C22×D3—44no—
619C22×D3—44no—
620C22×D3—44no—
621C22×D3—44no—
622C22×D3—44no—
623C22×D3C2×C3×D412yes—
624C22×D3C2×C3×D412yes—
625C22×D3C3×#4112yes—
626C22×D3C3×#4112yes—
627C22×D3C3×#4112yes—
628C3×D4—68no—
629C3×D4—124no—
630C3×D4—124no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—22no—
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—22no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—41no—
666C2×C3×C4—41no—
667C2×C3×C4—41no—
668C2×C3×C4—41no—
669C2×C3×C4—41no—
670C2×C3×C4—41no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
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—61no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—124no—
695C2×C3×C4—124no—
696C2×C3×C4—124no—
697C2×C3×C4C2×D1212yes—
698C2×C3×C4C2×D1212yes—
699C2×C3×C4D3×D412yes—
700C2×C3×C4C2×C3×D412yes—
701C2×C3×C4C2×C3×D412yes—
702C2×C3×C4C2×C3×D412yes—
703#67—44no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
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—
719D12—28no—
720D12—44no—
721C4×D3—44no—
722C4×D3—44no—
723C4×D3—44no—
724C2×C32—42no—
725C2×C32C2×#12311yescharacteristic
726C2×C32#52511yescharacteristic
727C2×C32#53811yescharacteristic
728C2×C32D4211yescharacteristic
729C2×C32#54611yescharacteristic
730C2×C32#54611yescharacteristic
731C2×C32#55111yescharacteristic
732C3×D3—24no—
733C3×D3—42no—
734C3×D3—42no—
735C24—31no—
736C24—31no—
737C24—31no—
738C24—62no—
739C24—62no—
740C24—62no—
741C24—62no—
742C24—62no—
743C24—121no—
744C24—121no—
745C24C22×C3×D311yescharacteristic
746C2×D4—34no—
747C2×D4—62no—
748C2×D4—62no—
749C2×D4—62no—
750C2×D4—62no—
751C2×D4—62no—
752C2×D4—62no—
753C2×D4—121no—
754C2×D4—121no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—62no—
761C22×C4—62no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—62no—
765C22×C4—62no—
766C22×C4—121no—
767C22×C4—121no—
768C22×C4—121no—
769C22×C4C22×C3×D311yescharacteristic
770C22×C4C22×C3×D311yescharacteristic
771C22×C4C22×C3×D311yescharacteristic
772C22×C4C22×C3×D311yescharacteristic
773C22×C4C22×C3×D311yescharacteristic
774C22×C4C22×C3×D311yescharacteristic
775C4⋊C4—41no—
776C4⋊C4—62no—
777C4⋊C4—62no—
778C4⋊C4—62no—
779C4⋊C4—121no—
780C22⋊C4—22no—
781C22⋊C4—41no—
782C22⋊C4—62no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—62no—
787C22⋊C4—62no—
788C22⋊C4—62no—
789C22⋊C4—62no—
790C22⋊C4—62no—
791C22⋊C4—62no—
792C22⋊C4—62no—
793C22⋊C4—121no—
794C22⋊C4—121no—
795C22⋊C4C3×D1214yescomplemented
796C42—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—34no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
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—81no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—1216no—
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×C3C22×D1211yescharacteristic
848C22×C3C2×D3×D411yescharacteristic
849C22×C3#100411yescharacteristic
850C22×C3D3×#4111yescharacteristic
851C22×C3D3×#4111yescharacteristic
852C22×C3D3×#4111yescharacteristic
853C22×C3#100911yescharacteristic
854C22×C3C22×C3×D411yescharacteristic
855C22×C3C22×C3×D411yescharacteristic
856C22×C3C2×C3×#4111yescharacteristic
857C22×C3C2×C3×#4111yescharacteristic
858C22×C3C2×C3×#4111yescharacteristic
859C22×C3C3×H(5,𝔽2)11yescharacteristic
860C22×C3C3×H(5,𝔽2)11yescharacteristic
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
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×D3C3×#12314yescomplemented
883C3×C4—22no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—22no—
887C3×C4—22no—
888C3×C4—22no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—41no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—81no—
900C3×C4—81no—
901C3×C4—121no—
902C3×C4—121no—
903C3×C4—121no—
904C3×C4—121no—
905C3×C4—121no—
906Dic3—41no—
907Dic3—41no—
908Dic3—41no—
909Dic3—41no—
910Dic3—41no—
911C32#241811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—68no—
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—124no—
941C23—124no—
942C23—124no—
943C23—124no—
944C23—124no—
945C23—124no—
946C23C2×C3×D1212yes—
947C23C23×C3×D311yescharacteristic
948D4—68no—
949D4—124no—
950D4—124no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
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—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—124no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4C2×C3×D1212yes—
985C2×C4C2×C3×D1212yes—
986C2×C4C3×D3×D412yes—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—64no—
997C2×C3—82no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3#552411yescharacteristic
1001C2×C3D4×D1211yescharacteristic
1002C2×C3#555411yescharacteristic
1003C2×C3#561211yescharacteristic
1004C2×C3D3×#12311yescharacteristic
1005C2×C3#567811yescharacteristic
1006C2×C3#570511yescharacteristic
1007C2×C3C2×C3×#12311yescharacteristic
1008C2×C3C3×#52511yescharacteristic
1009C2×C3C3×#53811yescharacteristic
1010C2×C3C3×D4211yescharacteristic
1011C2×C3C3×#54611yescharacteristic
1012C2×C3C3×#54611yescharacteristic
1013C2×C3C3×#55111yescharacteristic
1014D3—24no—
1015D3—42no—
1016D3—42no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—34no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—62no—
1036C22—62no—
1037C22—1216no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22—121no—
1045C22—121no—
1046C22C22×C3×D1211yescharacteristic
1047C22C2×C3×D3×D411yescharacteristic
1048C22C3×#100411yescharacteristic
1049C22C3×D3×#4111yescharacteristic
1050C22C3×D3×#4111yescharacteristic
1051C22C3×D3×#4111yescharacteristic
1052C22C3×#100911yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—121no—
1060C4—121no—
1061C4—121no—
1062C4—121no—
1063C4—121no—
1064C3—21no—
1065C3#7584411yescharacteristic, direct product factor
1066C3C3×#241811yescharacteristic, complemented
1067C2—42no—
1068C2—64no—
1069C2—122no—
1070C2—122no—
1071C2C3×#552411yescharacteristic
1072C2C3×D4×D1211yescharacteristic
1073C2C3×#555411yescharacteristic
1074C2C3×#561211yescharacteristic
1075C2C3×D3×#12311yescharacteristic
1076C2C3×#567811yescharacteristic
1077C2C3×#570511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC3×#388D3
hypocenterC3C3×#2418
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#883C2semidirect
3. C2×C3×D3×C22⋊C4C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C32×#388C2semidirect
6. C3×#4991C2semidirect
7. C3×#4987C2semidirect
8. C3×#4961C2semidirect
9. C3×#4955C2semidirect
10. C3×#4953C2semidirect
11. C3×#4940C2semidirect
12. C3×#4677C2semidirect
13. C3×#4668C2semidirect
14. C3×#4665C2semidirect
15. C3×#4665C2semidirect
17. #75844C3direct (N × H)
24. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
29. C2×C32×C42C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×C4⋊Dic3C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
61. C2×#883C2×C3semidirect
63. C2×D3×C22⋊C4C2×C3semidirect
64. C2×C4×D12C2×C3semidirect
71. C3×#388D3semidirect
72. C3×#388C2×C3semidirect
78. #4991C2×C3semidirect
79. #4987C2×C3semidirect
80. #4961C2×C3semidirect
81. #4955C2×C3semidirect
82. #4953C2×C3semidirect
83. #4940C2×C3semidirect
84. #4677C2×C3semidirect
85. #4668C2×C3semidirect
86. #4665C2×C3semidirect
87. #4665C2×C3semidirect
131. C32×C22⋊C4D4semidirect
164. C22×C4×D3C22×C3semidirect
173. C2×C3×C4⋊C4C2×D3semidirect
174. C2×C3×C4⋊C4C22×C3semidirect
199. C2×C3×C42C2×D3semidirect
200. C2×C3×C42C22×C3semidirect
211. C2×(C2×D3)⋊C4C22×C3semidirect
212. C2×(C2×D3)⋊C4C22×C3semidirect
213. C2×(C2×D3)⋊C4C22×C3semidirect
214. C2×C4⋊Dic3C22×C3semidirect
215. C2×C4⋊Dic3C22×C3semidirect
216. C2×C4⋊Dic3C22×C3semidirect
217. C2×Dic3⋊C4C22×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
320. #388C3×D3semidirect
440. C3×C22⋊C4D12semidirect
441. C3×C22⋊C4C3×D4semidirect
497. C2×C3×D3#123semidirect
523. C2×C4⋊C4C2×C3×D3semidirect
541. C2×C42C2×C3×D3semidirect
546. #95C2×C3×D3semidirect
547. #95C2×C3×D3semidirect
795. C22⋊C4C3×D12semidirect
882. C2×D3C3×#123semidirect
911. C32#2418semidirect
1065. C3#75844direct (N × H)
1066. C3C3×#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8832
C2×C3×#8822
C2×C3×D3×C22⋊C42
C2×C3×C4×D122
C32×#3882
C3×#49912
C3×#49872
C3×#49612
C3×#49552
C3×#49532
C3×#49402
C3×#46772
C3×#46682
C3×#46652
C3×#24183
#758443