Finite Group Databasebeta

← C3×#75840 #11807588

Subgroups — C3×#75840 #11807588

Order 1152.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic
2C32×#388C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic, complemented
4C3×#4988C211yesmaximal, characteristic, complemented
5C3×#4957C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7C3×#4955C211yesmaximal, characteristic, complemented
8C3×#4955C211yesmaximal, characteristic, complemented
9C3×#4951C211yesmaximal, characteristic, complemented
10C3×#4940C211yesmaximal, characteristic, complemented
11C3×#4939C211yesmaximal, characteristic, complemented
12C3×#4670C211yesmaximal, characteristic, complemented
13C3×#4669C211yesmaximal, characteristic, complemented
14C3×#4665C211yesmaximal, characteristic, complemented
15C3×#4665C211yesmaximal, characteristic, complemented
16C3×#2375—31nomaximal
17#75840C311yesmaximal, characteristic, direct product factor
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic, complemented
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×(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×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×C4×Dic3C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#882C418yescomplemented
48C32×#95C2211yescharacteristic, complemented
49C32×#95C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C2×C3×#120—31no—
55C2×#882C2×C311yescharacteristic
56C3×#390—31no—
57C3×#390—31no—
58C3×#390—31no—
59C3×#388—21no—
60C3×#388—31no—
61C3×#388—31no—
62C3×#388—31no—
63C3×#388—31no—
64C3×#388—31no—
65C3×#388D311yescharacteristic, complemented
66C3×#388C2×C311yescharacteristic, complemented
67C3×#386—31no—
68C3×#386—31no—
69C3×#386—31no—
70C3×#379—31no—
71C3×#379—31no—
72#4990C2×C311yescharacteristic, complemented
73#4988C2×C311yescharacteristic, complemented
74#4957C2×C311yescharacteristic, complemented
75#4956C2×C311yescharacteristic, complemented
76#4955C2×C311yescharacteristic, complemented
77#4955C2×C311yescharacteristic, complemented
78#4951C2×C311yescharacteristic, complemented
79#4940C2×C311yescharacteristic, complemented
80#4939C2×C311yescharacteristic, complemented
81#4670C2×C311yescharacteristic, complemented
82#4669C2×C311yescharacteristic, complemented
83#4665C2×C311yescharacteristic, complemented
84#4665C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C23×C3×D3—41no—
87C23×C3×D3—41no—
88C23×C3×D3—41no—
89C23×C3×D3—41no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3C2×C414yescomplemented
93C23×C3×D3C2311yescharacteristic
94C23×C3×D3C2311yescharacteristic
95C23×C3×D3C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C2×C3×#67—41no—
103C2×C3×#67—41no—
104C2×C3×#67C2×C414yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—41no—
111C2×C3×D12—41no—
112C2×C3×D12—41no—
113C2×C3×D12—41no—
114C2×C3×D12C2×C414yes—
115C2×C3×D12C2×C414yes—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×C3×C4×D3—41no—
119C32×C4⋊C4—41no—
120C32×C22⋊C4—41no—
121C32×C22⋊C4—41no—
122C32×C22⋊C4C2×C414yescomplemented
123C32×C42—41no—
124C3×#217—41no—
125C3×#217—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4—41no—
130C3×(C2×D3)⋊C4—41no—
131C3×(C2×D3)⋊C4—41no—
132C3×(C2×D3)⋊C4—41no—
133C3×(C2×D3)⋊C4—41no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4—41no—
137C3×(C2×D3)⋊C4C2×C414yescomplemented
138C3×(C2×D3)⋊C4C2×C414yescomplemented
139C3×C4⋊Dic3—41no—
140C3×Dic3⋊C4—41no—
141C3×C4×Dic3—41no—
142C3×C4×Dic3—41no—
143#2375—31noSylow
144C25×C3—31no—
145C24×D3C22×C311yescharacteristic
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—31no—
149C23×C3×C4—31no—
150C22×#67C22×C311yescharacteristic
151C22×D12C22×C311yescharacteristic
152C22×D12C22×C311yescharacteristic
153C22×C4×D3C22×C311yescharacteristic, complemented
154C3×#120—38no—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
159C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
179C2×C3×C22⋊C4C2×D311yescharacteristic
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C22⋊C4C22×C311yescharacteristic
182C2×C3×C22⋊C4C22×C311yescharacteristic
183C2×C3×C22⋊C4C22×C311yescharacteristic
184C2×C3×C42—21no—
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×C3×C42C2×D311yescharacteristic, complemented
188C2×C3×C42C22×C311yescharacteristic, complemented
189C2×#217C22×C311yescharacteristic
190C2×#217C22×C311yescharacteristic
191C2×(C2×D3)⋊C4C22×C311yescharacteristic
192C2×(C2×D3)⋊C4C22×C311yescharacteristic
193C2×(C2×D3)⋊C4C22×C311yescharacteristic
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, complemented
202C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
203C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
204C2×C4⋊Dic3C22×C311yescharacteristic, complemented
205C2×Dic3⋊C4C22×C311yescharacteristic, complemented
206C2×C4×Dic3C22×C311yescharacteristic, complemented
207C2×C4×Dic3C22×C311yescharacteristic, complemented
208#882C3×C418yescomplemented
209C3×#95—21no—
210C3×#95—21no—
211C3×#95—31no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95C2×D311yescharacteristic, complemented
216C3×#95C2×D311yescharacteristic, complemented
217C3×#95C22×C311yescharacteristic, complemented
218C3×#95C22×C311yescharacteristic, complemented
219C3⋊#95C22×C311yescharacteristic, complemented
220C3⋊#95C22×C311yescharacteristic, complemented
221C3⋊#95C22×C311yescharacteristic, complemented
222C3⋊#95C22×C311yescharacteristic, complemented
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C2411yescharacteristic
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
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×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—44no—
250C22×C3×D3—44no—
251C22×C3×D3—44no—
252C22×C3×D3—44no—
253C22×C3×D3—44no—
254C22×C3×D3—44no—
255C22×C3×D3—44no—
256C22×C3×D3C22×C412yes—
257C22×C3×D3C22×C412yes—
258C22×C3×D3C22×C412yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4C22×C412yes—
276C2×C32×C4C22×C412yes—
277C3×#67—44no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3C22×C412yes—
293C3×D12—44no—
294C3×D12—44no—
295C3×C4×D3—44no—
296C2×#120—31no—
297#390—31no—
298#390—31no—
299#390—31no—
300#388—31no—
301#388—31no—
302#388—31no—
303#388—31no—
304#388—31no—
305#388C3×D311yescharacteristic, complemented
306#386—31no—
307#386—31no—
308#386—31no—
309#379—31no—
310#379—31no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3—31no—
314C24×C3—31no—
315C24×C3—34no—
316C24×C3—121no—
317C24×C3—121no—
318C24×C3—121no—
319C24×C3—121no—
320C24×C3—121no—
321C24×C3—121no—
322C24×C3C22×D311yescharacteristic
323C24×C3C23×C311yescharacteristic
324C23×D3—41no—
325C23×D3—41no—
326C23×D3—41no—
327C23×D3—41no—
328C23×D3—41no—
329C23×D3—41no—
330C23×D3C2×C3×C414yescomplemented
331C23×D3C23×C311yescharacteristic
332C23×D3C23×C311yescharacteristic
333C23×D3C23×C311yescharacteristic
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—121no—
338C2×C3×D4—121no—
339C2×C3×D4—121no—
340C2×C3×D4—121no—
341C2×C3×D4—121no—
342C2×C3×D4—121no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—121no—
355C22×C3×C4—121no—
356C22×C3×C4—121no—
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C23×C311yescharacteristic
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C22×C3×C4C23×C311yescharacteristic
368C22×C3×C4C23×C311yescharacteristic
369C2×#67—41no—
370C2×#67—41no—
371C2×#67C2×C3×C414yes—
372C22×Dic3C23×C311yescharacteristic
373C22×Dic3C23×C311yescharacteristic
374C22×Dic3C23×C311yescharacteristic
375C22×Dic3C23×C311yescharacteristic
376C22×Dic3C23×C311yescharacteristic
377C2×D12—41no—
378C2×D12—41no—
379C2×D12—41no—
380C2×D12—41no—
381C2×D12C2×C3×C414yes—
382C2×D12C2×C3×C414yes—
383C2×C4×D3—41no—
384C2×C4×D3—41no—
385C2×C4×D3—41no—
386C3×C4⋊C4—41no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—42no—
389C3×C4⋊C4—121no—
390C3×C4⋊C4—121no—
391C3×C22⋊C4—24no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—41no—
398C3×C22⋊C4—42no—
399C3×C22⋊C4—42no—
400C3×C22⋊C4—121no—
401C3×C22⋊C4—121no—
402C3×C22⋊C4—121no—
403C3×C22⋊C4—121no—
404C3×C22⋊C4—121no—
405C3×C22⋊C4—121no—
406C3×C22⋊C4—121no—
407C3×C22⋊C4—121no—
408C3×C22⋊C4—121no—
409C3×C22⋊C4—121no—
410C3×C22⋊C4—121no—
411C3×C22⋊C4—121no—
412C3×C22⋊C4—121no—
413C3×C22⋊C4C4×D314yescomplemented
414C3×C22⋊C4C2×C3×C414yescomplemented
415C3×C42—41no—
416C3×C42—41no—
417C3×C42—42no—
418C3×C42—121no—
419C3×C42—121no—
420#217—41no—
421#217—41no—
422(C2×D3)⋊C4—41no—
423(C2×D3)⋊C4—41no—
424(C2×D3)⋊C4—41no—
425(C2×D3)⋊C4—41no—
426(C2×D3)⋊C4—41no—
427(C2×D3)⋊C4—41no—
428(C2×D3)⋊C4—41no—
429(C2×D3)⋊C4—41no—
430(C2×D3)⋊C4—41no—
431(C2×D3)⋊C4—41no—
432(C2×D3)⋊C4—41no—
433(C2×D3)⋊C4C2×C3×C414yescomplemented
434(C2×D3)⋊C4C2×C3×C414yescomplemented
435C4⋊Dic3—41no—
436Dic3⋊C4—41no—
437C4×Dic3—41no—
438C4×Dic3—41no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32C23×C411yescharacteristic
447C22×C32H(5,𝔽2)11yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C22×C32H(5,𝔽2)11yescharacteristic
451C22×C32H(5,𝔽2)11yescharacteristic
452C22×C32H(5,𝔽2)11yescharacteristic
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—416no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C32×C4—22no—
476C32×C4—22no—
477C32×C4—41no—
478C32×C4—41no—
479C32×C4—41no—
480C32×C4—41no—
481C3×Dic3—22no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C25—31no—
487C22×D4—31no—
488C22×D4—31no—
489C22×D4—31no—
490C23×C4—31no—
491#120—38no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—31no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4C2×C3×D311yescharacteristic
511C2×C22⋊C4C2×C3×D311yescharacteristic
512C2×C22⋊C4C2×C3×D311yescharacteristic
513C2×C42—31no—
514C2×C42—31no—
515C2×C42C2×C3×D311yescharacteristic, complemented
516#95—31no—
517#95—31no—
518#95—31no—
519#95—31no—
520#95C2×C3×D311yescharacteristic, complemented
521#95C2×C3×D311yescharacteristic, complemented
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—124no—
564C23×C3—124no—
565C23×C3—124no—
566C23×C3—124no—
567C23×C3—124no—
568C23×C3—124no—
569C23×C3—124no—
570C23×C3C2×C4×D312yes—
571C23×C3C22×C3×C412yes—
572C23×C3C23×D311yescharacteristic
573C23×C3C24×C311yescharacteristic
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—44no—
593C22×D3—44no—
594C22×D3—44no—
595C22×D3—44no—
596C22×D3—44no—
597C22×D3—44no—
598C22×D3—44no—
599C22×D3C22×C3×C412yes—
600C22×D3C22×C3×C412yes—
601C22×D3C22×C3×C412yes—
602C3×D4—124no—
603C3×D4—124no—
604C3×D4—124no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
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—22no—
640C2×C3×C4—22no—
641C2×C3×C4—32no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—124no—
671C2×C3×C4C2×C4×D312yes—
672C2×C3×C4C2×C4×D312yes—
673C2×C3×C4C22×C3×C412yes—
674C2×C3×C4C22×C3×C412yes—
675#67—44no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3C22×C3×C412yes—
691D12—44no—
692D12—44no—
693C4×D3—44no—
694C2×C32—42no—
695C2×C32#51811yescharacteristic
696C2×C32#51811yescharacteristic
697C2×C32#51811yescharacteristic
698C2×C32#56011yescharacteristic
699C2×C32#56011yescharacteristic
700C2×C32#56011yescharacteristic
701C2×C32H(3,𝔽4)11yescharacteristic
702C3×D3—42no—
703C3×D3—42no—
704C3×D3—42no—
705C24—31no—
706C24—31no—
707C24—31no—
708C24—34no—
709C24—121no—
710C24—121no—
711C24—121no—
712C24—121no—
713C24—121no—
714C24—121no—
715C24C22×C3×D311yescharacteristic
716C2×D4—34no—
717C2×D4—34no—
718C2×D4—34no—
719C2×D4—121no—
720C2×D4—121no—
721C2×D4—121no—
722C2×D4—121no—
723C2×D4—121no—
724C2×D4—121no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—121no—
731C22×C4—121no—
732C22×C4—121no—
733C22×C4C22×C3×D311yescharacteristic
734C22×C4C22×C3×D311yescharacteristic
735C22×C4C22×C3×D311yescharacteristic
736C22×C4C22×C3×D311yescharacteristic
737C22×C4C22×C3×D311yescharacteristic
738C22×C4C22×C3×D311yescharacteristic
739C4⋊C4—41no—
740C4⋊C4—121no—
741C4⋊C4—121no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—41no—
745C22⋊C4—41no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C22⋊C4—121no—
749C22⋊C4—121no—
750C22⋊C4—121no—
751C22⋊C4—121no—
752C22⋊C4—121no—
753C22⋊C4—121no—
754C22⋊C4—121no—
755C22⋊C4—121no—
756C22⋊C4—121no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4C3×C4×D314yescomplemented
760C42—41no—
761C42—121no—
762C42—121no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—42no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—81no—
797C22×C3—81no—
798C22×C3—81no—
799C22×C3—81no—
800C22×C3—1216no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3C22×C4×D311yescharacteristic
814C22×C3#100411yescharacteristic
815C22×C3#100411yescharacteristic
816C22×C3#100911yescharacteristic
817C22×C3#100911yescharacteristic
818C22×C3#100911yescharacteristic
819C22×C3#100911yescharacteristic
820C22×C3C23×C3×C411yescharacteristic
821C22×C3C3×H(5,𝔽2)11yescharacteristic
822C22×C3C3×H(5,𝔽2)11yescharacteristic
823C22×C3C3×H(5,𝔽2)11yescharacteristic
824C22×C3C3×H(5,𝔽2)11yescharacteristic
825C22×C3C3×H(5,𝔽2)11yescharacteristic
826C22×C3C3×H(5,𝔽2)11yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—416no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—42no—
854C3×C4—42no—
855C3×C4—42no—
856C3×C4—42no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—62no—
866C3×C4—81no—
867C3×C4—81no—
868C3×C4—121no—
869C3×C4—121no—
870C3×C4—121no—
871C3×C4—121no—
872Dic3—22no—
873Dic3—41no—
874Dic3—41no—
875Dic3—41no—
876Dic3—41no—
877C32#237511yescharacteristic, complemented, Sylow
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—21no—
883C23—21no—
884C23—32no—
885C23—32no—
886C23—32no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—124no—
906C23—124no—
907C23—124no—
908C23—124no—
909C23—124no—
910C23—124no—
911C23—124no—
912C23C2×C3×C4×D312yes—
913C23C23×C3×D311yescharacteristic
914D4—124no—
915D4—124no—
916D4—124no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—32no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—61no—
947C2×C4—61no—
948C2×C4—124no—
949C2×C4C2×C3×C4×D312yes—
950C2×C4C2×C3×C4×D312yes—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—42no—
959C2×C3—42no—
960C2×C3—82no—
961C2×C3—122no—
962C2×C3—122no—
963C2×C3—122no—
964C2×C3#552111yescharacteristic
965C2×C3#554511yescharacteristic
966C2×C3#554511yescharacteristic
967C2×C3#562011yescharacteristic
968C2×C3#566611yescharacteristic
969C2×C3#568311yescharacteristic
970C2×C3#571111yescharacteristic
971C2×C3C3×#51811yescharacteristic
972C2×C3C3×#51811yescharacteristic
973C2×C3C3×#51811yescharacteristic
974C2×C3C3×#56011yescharacteristic
975C2×C3C3×#56011yescharacteristic
976C2×C3C3×#56011yescharacteristic
977C2×C3C3×H(3,𝔽4)11yescharacteristic
978D3—42no—
979D3—42no—
980D3—42no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—41no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—1216no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22C22×C3×C4×D311yescharacteristic
1011C22C3×#100411yescharacteristic
1012C22C3×#100411yescharacteristic
1013C22C3×#100911yescharacteristic
1014C22C3×#100911yescharacteristic
1015C22C3×#100911yescharacteristic
1016C22C3×#100911yescharacteristic
1017C4—22no—
1018C4—22no—
1019C4—41no—
1020C4—41no—
1021C4—41no—
1022C4—41no—
1023C4—62no—
1024C4—121no—
1025C4—121no—
1026C4—121no—
1027C4—121no—
1028C3—21no—
1029C3#7584011yescharacteristic, direct product factor
1030C3C3×#237511yescharacteristic, complemented
1031C2—42no—
1032C2—122no—
1033C2—122no—
1034C2—122no—
1035C2C3×#552111yescharacteristic
1036C2C3×#554511yescharacteristic
1037C2C3×#554511yescharacteristic
1038C2C3×#562011yescharacteristic
1039C2C3×#566611yescharacteristic
1040C2C3×#568311yescharacteristic
1041C2C3×#571111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC2×C3×#882C2
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×#2375
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
2. C32×#388C2semidirect
3. C3×#4990C2semidirect
4. C3×#4988C2semidirect
5. C3×#4957C2semidirect
6. C3×#4956C2semidirect
7. C3×#4955C2semidirect
8. C3×#4955C2semidirect
9. C3×#4951C2semidirect
10. C3×#4940C2semidirect
11. C3×#4939C2semidirect
12. C3×#4670C2semidirect
13. C3×#4669C2semidirect
14. C3×#4665C2semidirect
15. C3×#4665C2semidirect
17. #75840C3direct (N × H)
22. C22×C3×C4×D3C22semidirect
23. C2×C32×C4⋊C4C22semidirect
27. 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×Dic3⋊C4C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#882C4semidirect
48. C32×#95C22semidirect
49. C32×#95C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
65. C3×#388D3semidirect
66. C3×#388C2×C3semidirect
72. #4990C2×C3semidirect
73. #4988C2×C3semidirect
74. #4957C2×C3semidirect
75. #4956C2×C3semidirect
76. #4955C2×C3semidirect
77. #4955C2×C3semidirect
78. #4951C2×C3semidirect
79. #4940C2×C3semidirect
80. #4939C2×C3semidirect
81. #4670C2×C3semidirect
82. #4669C2×C3semidirect
83. #4665C2×C3semidirect
84. #4665C2×C3semidirect
92. C23×C3×D3C2×C4semidirect
122. C32×C22⋊C4C2×C4semidirect
137. C3×(C2×D3)⋊C4C2×C4semidirect
138. C3×(C2×D3)⋊C4C2×C4semidirect
153. C22×C4×D3C22×C3semidirect
158. C2×C3×C4⋊C4C2×D3semidirect
159. C2×C3×C4⋊C4C22×C3semidirect
187. C2×C3×C42C2×D3semidirect
188. C2×C3×C42C22×C3semidirect
201. C2×(C2×D3)⋊C4C22×C3semidirect
202. C2×(C2×D3)⋊C4C22×C3semidirect
203. C2×(C2×D3)⋊C4C22×C3semidirect
204. C2×C4⋊Dic3C22×C3semidirect
205. C2×Dic3⋊C4C22×C3semidirect
206. C2×C4×Dic3C22×C3semidirect
207. C2×C4×Dic3C22×C3semidirect
208. #882C3×C4semidirect
215. C3×#95C2×D3semidirect
216. C3×#95C2×D3semidirect
217. C3×#95C22×C3semidirect
218. C3×#95C22×C3semidirect
219. C3⋊#95C22×C3semidirect
220. C3⋊#95C22×C3semidirect
221. C3⋊#95C22×C3semidirect
222. C3⋊#95C22×C3semidirect
305. #388C3×D3semidirect
330. C23×D3C2×C3×C4semidirect
413. C3×C22⋊C4C4×D3semidirect
414. C3×C22⋊C4C2×C3×C4semidirect
433. (C2×D3)⋊C4C2×C3×C4semidirect
434. (C2×D3)⋊C4C2×C3×C4semidirect
494. C2×C4⋊C4C2×C3×D3semidirect
515. C2×C42C2×C3×D3semidirect
520. #95C2×C3×D3semidirect
521. #95C2×C3×D3semidirect
759. C22⋊C4C3×C4×D3semidirect
877. C32#2375semidirect
1029. C3#75840direct (N × H)
1030. C3C3×#2375semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8822
C32×#3882
C3×#49902
C3×#49882
C3×#49572
C3×#49562
C3×#49552
C3×#49512
C3×#49402
C3×#49392
C3×#46702
C3×#46692
C3×#46652
C3×#23753
#758403