Finite Group Databasebeta

← C2×C3×#5705 #11902871

Subgroups — C2×C3×#5705 #11902871

Order 1152.

2779 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C3×#5705C2116yesmaximal, direct product factor
3C2×C3×#897C211yesmaximal, characteristic, complemented
4C2×C3×#896C211yesmaximal, characteristic, complemented
5C2×C3×#894C211yesmaximal, characteristic, complemented
6C2×C3×#894C211yesmaximal, characteristic, complemented
7C2×C3×#893C211yesmaximal, characteristic, complemented
8C2×C3×#892C211yesmaximal, characteristic, complemented
9C2×C3×#885C211yesmaximal, characteristic, complemented
10C2×C3×#883C211yesmaximal, characteristic, complemented
11C2×C3×#882C211yesmaximal, characteristic
12C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
13C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
14C2×C3×#879C211yesmaximal, characteristic, complemented
15C2×C3×C4×D12C211yesmaximal, characteristic, complemented
16C2×C3×#872C211yesmaximal, characteristic, complemented
17C2×C3×#551—31nomaximal
18C2×#5705C311yesmaximal, characteristic, direct product factor
19C24×C3×D3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×Dic6C2211yescharacteristic, complemented
29C32×#126C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic, complemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×C32×C42C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
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, complemented
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53C2×C3×C4×Dic3C2211yescharacteristic, complemented
54C2×C3×C4×Dic3C2211yescharacteristic, complemented
55C3×#897C2218yescomplemented
56C3×#896C2218yescomplemented
57C3×#894C2218yescomplemented
58C3×#894C2218yescomplemented
59C3×#893C2218yescomplemented
60C3×#892C2218yescomplemented
61C3×#885C2218yescomplemented
62C3×#883C2218yescomplemented
63C3×#882C2218yes—
64C3×D3×C22⋊C4C2218yescomplemented
65C3×D3×C22⋊C4C2218yescomplemented
66C3×#879C2218yescomplemented
67C3×C4×D12C2218yescomplemented
68C3×#872C2218yescomplemented
69C3×#551—316no—
70C2×C3×#126—21no—
71C2×C3×#126—31no—
72C2×C3×#126D311yescharacteristic, complemented
73C2×C3×#126C2×C311yescharacteristic, complemented
74C2×C3×#124—31no—
75C2×C3×#123—31no—
76C2×C3×#123—31no—
77C2×C3×#123—31no—
78C2×C3×C22⋊Q8—31no—
79C2×C3×C22⋊Q8—31no—
80C2×C3×#120—31no—
81C2×C3×C4×D4—31no—
82C2×C3×C4×D4—31no—
83C2×C3×#117—31no—
84C2×C3×#117—31no—
85C22×C3×C22⋊C4—31no—
86C22×C3×C22⋊C4—31no—
87#5705C2×C3116yesdirect product factor
88C2×#897C2×C311yescharacteristic, complemented
89C2×#896C2×C311yescharacteristic, complemented
90C2×#894C2×C311yescharacteristic, complemented
91C2×#894C2×C311yescharacteristic, complemented
92C2×#893C2×C311yescharacteristic, complemented
93C2×#892C2×C311yescharacteristic, complemented
94C2×#885C2×C311yescharacteristic, complemented
95C2×#883C2×C311yescharacteristic, complemented
96C2×#882C2×C311yescharacteristic
97C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
98C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
99C2×#879C2×C311yescharacteristic, complemented
100C2×C4×D12C2×C311yescharacteristic, complemented
101C2×#872C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3×D3—24no—
104C23×C3×D3—24no—
105C23×C3×D3—42no—
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2314yes—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C2×C3×#67—42no—
117C2×C3×#67C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—24no—
124C2×C3×D12—24no—
125C2×C3×D12C2314yes—
126C2×C3×D12C2314yes—
127C2×C3×C4×D3—24no—
128C2×C3×C4×D3—24no—
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2314yescomplemented
137C2×C3×Dic6—42no—
138C2×C3×Dic6C2314yescomplemented
139C32×C4⋊C4C2314yescomplemented
140C32×C4⋊C4C2314yescomplemented
141C32×C4⋊C4C2314yescomplemented
142C32×C22⋊C4C2314yes—
143C32×C22⋊C4C2314yes—
144C32×C22⋊C4C2314yes—
145C32×C42C2314yescomplemented
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×(C2×D3)⋊C4C2314yescomplemented
156C3×(C2×D3)⋊C4C2314yescomplemented
157C3×C4⋊Dic3C2314yescomplemented
158C3×C4⋊Dic3C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160C3×Dic3⋊C4C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162C3×C4×Dic3C2314yescomplemented
163C3×C4×Dic3C2314yescomplemented
164C2×#551—31noSylow
165C25×C3—31no—
166C24×D3C22×C311yescharacteristic
167C22×C3×Q8—31no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C23×C3×C4—31no—
176C22×#67C22×C311yescharacteristic
177C22×D12C22×C311yescharacteristic
178C22×D12C22×C311yescharacteristic
179C22×C4×D3C22×C311yescharacteristic
180C22×C4×D3C22×C311yescharacteristic
181C22×C4×D3C22×C311yescharacteristic
182C22×C4×D3C22×C311yescharacteristic
183C22×C4×D3C22×C311yescharacteristic, complemented
184C22×Dic6C22×C311yescharacteristic, complemented
185C3×#126—28no—
186C3×#126—38no—
187C3×#126C2×D318yescomplemented
188C3×#126C22×C318yescomplemented
189C3×#124—38no—
190C3×#123—38no—
191C3×#123—38no—
192C3×#123—38no—
193C3×C22⋊Q8—38no—
194C3×C22⋊Q8—38no—
195C3×#120—38no—
196C3×C4×D4—38no—
197C3×C4×D4—38no—
198C3×#117—38no—
199C3×#117—38no—
200C2×C3×C4⋊C4—21no—
201C2×C3×C4⋊C4—21no—
202C2×C3×C4⋊C4—21no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
209C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
210C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
211C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
212C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
213C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
214C2×C3×C22⋊C4—21no—
215C2×C3×C22⋊C4—21no—
216C2×C3×C22⋊C4—21no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—31no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—38no—
229C2×C3×C22⋊C4—38no—
230C2×C3×C22⋊C4C2×D311yescharacteristic
231C2×C3×C22⋊C4C2×D311yescharacteristic
232C2×C3×C22⋊C4C2×D311yescharacteristic
233C2×C3×C22⋊C4C22×C311yescharacteristic
234C2×C3×C22⋊C4C22×C311yescharacteristic
235C2×C3×C22⋊C4C22×C311yescharacteristic
236C2×C3×C42—21no—
237C2×C3×C42—31no—
238C2×C3×C42—31no—
239C2×C3×C42C2×D311yescharacteristic, complemented
240C2×C3×C42C22×C311yescharacteristic, complemented
241C2×#217C22×C311yescharacteristic
242C2×#217C22×C311yescharacteristic
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×(C2×D3)⋊C4C22×C311yescharacteristic
245C2×(C2×D3)⋊C4C22×C311yescharacteristic
246C2×(C2×D3)⋊C4C22×C311yescharacteristic
247C2×(C2×D3)⋊C4C22×C311yescharacteristic
248C2×(C2×D3)⋊C4C22×C311yescharacteristic
249C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
250C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
251C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
252C2×C4⋊Dic3C22×C311yescharacteristic, complemented
253C2×C4⋊Dic3C22×C311yescharacteristic, complemented
254C2×Dic3⋊C4C22×C311yescharacteristic, complemented
255C2×Dic3⋊C4C22×C311yescharacteristic, complemented
256C2×Dic3⋊C4C22×C311yescharacteristic, complemented
257C2×C4×Dic3C22×C311yescharacteristic, complemented
258C2×C4×Dic3C22×C311yescharacteristic, complemented
259#897C22×C318yescomplemented
260#896C22×C318yescomplemented
261#894C22×C318yescomplemented
262#894C22×C318yescomplemented
263#893C22×C318yescomplemented
264#892C22×C318yescomplemented
265#885C22×C318yescomplemented
266#883C22×C318yescomplemented
267#882C22×C318yes—
268D3×C22⋊C4C22×C318yescomplemented
269D3×C22⋊C4C22×C318yescomplemented
270#879C22×C318yescomplemented
271C4×D12C22×C318yescomplemented
272#872C22×C318yescomplemented
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—44no—
288C22×C3×D3—416no—
289C22×C3×D3#4114yes—
290C22×C3×D3#4114yes—
291C22×C3×D3C2412yes—
292C22×C3×D3C2412yes—
293C22×C3×D3C2412yes—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4—22no—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4—22no—
300C2×C32×C4C2412yes—
301C2×C32×C4C2412yes—
302C2×C32×C4C2412yes—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C3×#67—44no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×D12—28no—
318C3×D12—28no—
319C3×C4×D3—28no—
320C3×C4×D3—28no—
321C3×C4×D3—44no—
322C3×C4×D3—44no—
323C3×C4×D3—44no—
324C3×Dic6—44no—
325#551—316no—
326C2×#126—31no—
327C2×#126C3×D311yescharacteristic, complemented
328C2×#124—31no—
329C2×#123—31no—
330C2×#123—31no—
331C2×#123—31no—
332C2×C22⋊Q8—31no—
333C2×C22⋊Q8—31no—
334C2×#120—31no—
335C2×C4×D4—31no—
336C2×C4×D4—31no—
337C2×#117—31no—
338C2×#117—31no—
339C22×C22⋊C4—31no—
340C22×C22⋊C4—31no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3—31no—
344C24×C3—31no—
345C24×C3—34no—
346C24×C3—64no—
347C24×C3—64no—
348C24×C3—122no—
349C24×C3C22×D311yescharacteristic
350C24×C3C23×C311yescharacteristic
351C23×D3—24no—
352C23×D3—24no—
353C23×D3—42no—
354C23×D3C23×C311yescharacteristic
355C23×D3C23×C314yes—
356C23×D3C23×C311yescharacteristic
357C23×D3C23×C311yescharacteristic
358C2×C3×Q8—34no—
359C2×C3×Q8—122no—
360C2×C3×D4—34no—
361C2×C3×D4—34no—
362C2×C3×D4—34no—
363C2×C3×D4—64no—
364C2×C3×D4—64no—
365C2×C3×D4—122no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—34no—
378C22×C3×C4—34no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—64no—
383C22×C3×C4—64no—
384C22×C3×C4—122no—
385C22×C3×C4—122no—
386C22×C3×C4—122no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C23×C311yescharacteristic
394C22×C3×C4C23×C311yescharacteristic
395C22×C3×C4C23×C311yescharacteristic
396C22×C3×C4C23×C311yescharacteristic
397C22×C3×C4C23×C311yescharacteristic
398C22×C3×C4C23×C311yescharacteristic
399C2×#67—42no—
400C2×#67C23×C314yes—
401C22×Dic3C23×C311yescharacteristic
402C22×Dic3C23×C311yescharacteristic
403C22×Dic3C23×C311yescharacteristic
404C22×Dic3C23×C311yescharacteristic
405C22×Dic3C23×C311yescharacteristic
406C2×D12—24no—
407C2×D12—24no—
408C2×D12C23×C314yes—
409C2×D12C23×C314yes—
410C2×C4×D3—24no—
411C2×C4×D3—24no—
412C2×C4×D3—42no—
413C2×C4×D3—42no—
414C2×C4×D3—42no—
415C2×C4×D3C23×C314yes—
416C2×C4×D3C23×C314yes—
417C2×C4×D3C23×C314yes—
418C2×C4×D3C23×C314yes—
419C2×C4×D3C23×C314yescomplemented
420C2×Dic6—42no—
421C2×Dic6C23×C314yescomplemented
422C3×C4⋊C4—24no—
423C3×C4⋊C4—24no—
424C3×C4⋊C4—24no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4C22×D314yescomplemented
431C3×C4⋊C4C22×D314yescomplemented
432C3×C4⋊C4C22×D314yescomplemented
433C3×C4⋊C4C23×C314yescomplemented
434C3×C4⋊C4C23×C314yescomplemented
435C3×C4⋊C4C23×C314yescomplemented
436C3×C22⋊C4—24no—
437C3×C22⋊C4—24no—
438C3×C22⋊C4—24no—
439C3×C22⋊C4—34no—
440C3×C22⋊C4—34no—
441C3×C22⋊C4—34no—
442C3×C22⋊C4—34no—
443C3×C22⋊C4—34no—
444C3×C22⋊C4—34no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4C22×D314yes—
451C3×C22⋊C4C22×D314yes—
452C3×C22⋊C4C22×D314yes—
453C3×C22⋊C4C23×C314yes—
454C3×C22⋊C4C23×C314yes—
455C3×C22⋊C4C23×C314yes—
456C3×C42—24no—
457C3×C42—34no—
458C3×C42—34no—
459C3×C42C22×D314yescomplemented
460C3×C42C23×C314yescomplemented
461#217C23×C314yes—
462#217C23×C314yes—
463(C2×D3)⋊C4C23×C314yes—
464(C2×D3)⋊C4C23×C314yes—
465(C2×D3)⋊C4C23×C314yes—
466(C2×D3)⋊C4C23×C314yes—
467(C2×D3)⋊C4C23×C314yes—
468(C2×D3)⋊C4C23×C314yes—
469(C2×D3)⋊C4C23×C314yescomplemented
470(C2×D3)⋊C4C23×C314yescomplemented
471(C2×D3)⋊C4C23×C314yescomplemented
472C4⋊Dic3C23×C314yescomplemented
473C4⋊Dic3C23×C314yescomplemented
474Dic3⋊C4C23×C314yescomplemented
475Dic3⋊C4C23×C314yescomplemented
476Dic3⋊C4C23×C314yescomplemented
477C4×Dic3C23×C314yescomplemented
478C4×Dic3C23×C314yescomplemented
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—44no—
483C22×C32C2×#4112yes—
484C22×C32C2×#4112yes—
485C22×C32H(5,𝔽2)12yes—
486C22×C32C2511yescharacteristic
487C2×C3×D3—28no—
488C2×C3×D3—28no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—416no—
497C2×C3×D3—44no—
498C2×C3×D3C2×#4114yes—
499C2×C3×D3C2×#4114yes—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4—22no—
504C32×C4—22no—
505C32×C4—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C25—31no—
512C22×Q8—31no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—31no—
521#126—38no—
522#126C2×C3×D318yescomplemented
523#124—38no—
524#123—38no—
525#123—38no—
526#123—38no—
527C22⋊Q8—38no—
528C22⋊Q8—38no—
529#120—38no—
530C4×D4—38no—
531C4×D4—38no—
532#117—38no—
533#117—38no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
540C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
541C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
542C2×C22⋊C4—31no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—38no—
554C2×C22⋊C4—38no—
555C2×C22⋊C4C2×C3×D311yescharacteristic
556C2×C22⋊C4C2×C3×D311yescharacteristic
557C2×C22⋊C4C2×C3×D311yescharacteristic
558C2×C42—31no—
559C2×C42—31no—
560C2×C42C2×C3×D311yescharacteristic, complemented
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—21no—
568C23×C3—22no—
569C23×C3—34no—
570C23×C3—34no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—68no—
578C23×C3—68no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—124no—
587C23×C3—1216no—
588C23×C3C23×D312yes—
589C23×C3C23×D311yescharacteristic
590C23×C3C24×C312yes—
591C23×C3C24×C311yescharacteristic
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—22no—
598C22×D3—22no—
599C22×D3—28no—
600C22×D3—28no—
601C22×D3—44no—
602C22×D3—416no—
603C22×D3C3×#4114yes—
604C22×D3C3×#4114yes—
605C22×D3C24×C312yes—
606C22×D3C24×C312yes—
607C22×D3C24×C312yes—
608C3×Q8—124no—
609C3×D4—68no—
610C3×D4—68no—
611C3×D4—124no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—42no—
636C2×C3×C4—42no—
637C2×C3×C4—42no—
638C2×C3×C4—42no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—68no—
642C2×C3×C4—68no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—124no—
649C2×C3×C4—124no—
650C2×C3×C4—124no—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C24×C312yes—
658C2×C3×C4C24×C312yes—
659C2×C3×C4C24×C312yes—
660C2×C3×C4C24×C312yes—
661C2×C3×C4C24×C312yes—
662C2×C3×C4C24×C312yes—
663#67—44no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—22no—
668C2×Dic3—22no—
669C2×Dic3C24×C312yes—
670C2×Dic3C24×C312yes—
671C2×Dic3C24×C312yes—
672C2×Dic3C24×C312yes—
673C2×Dic3C24×C312yes—
674D12—28no—
675D12—28no—
676C4×D3—28no—
677C4×D3—28no—
678C4×D3—44no—
679C4×D3—44no—
680C4×D3—44no—
681Dic6—44no—
682C2×C32—42no—
683C2×C32#55114yescomplemented
684C2×C32C22×#4111yescharacteristic
685C2×C32C22×#4111yescharacteristic
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C3×D3—24no—
688C3×D3—24no—
689C3×D3—42no—
690C24—31no—
691C24—31no—
692C24—31no—
693C24—34no—
694C24—64no—
695C24—64no—
696C24—122no—
697C24C22×C3×D311yescharacteristic
698C2×Q8—34no—
699C2×Q8—122no—
700C2×D4—34no—
701C2×D4—34no—
702C2×D4—34no—
703C2×D4—64no—
704C2×D4—64no—
705C2×D4—122no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—34no—
712C22×C4—34no—
713C22×C4—34no—
714C22×C4—34no—
715C22×C4—34no—
716C22×C4—64no—
717C22×C4—64no—
718C22×C4—122no—
719C22×C4—122no—
720C22×C4—122no—
721C22×C4C22×C3×D311yescharacteristic
722C22×C4C22×C3×D311yescharacteristic
723C22×C4C22×C3×D311yescharacteristic
724C22×C4C22×C3×D311yescharacteristic
725C22×C4C22×C3×D311yescharacteristic
726C22×C4C22×C3×D311yescharacteristic
727C4⋊C4—34no—
728C4⋊C4—34no—
729C4⋊C4—34no—
730C4⋊C4—34no—
731C4⋊C4—34no—
732C4⋊C4C22×C3×D314yescomplemented
733C4⋊C4C22×C3×D314yescomplemented
734C4⋊C4C22×C3×D314yescomplemented
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4C22×C3×D314yes—
747C22⋊C4C22×C3×D314yes—
748C22⋊C4C22×C3×D314yes—
749C42—34no—
750C42—34no—
751C42C22×C3×D314yescomplemented
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—21no—
762C22×C3—34no—
763C22×C3—34no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—44no—
768C22×C3—44no—
769C22×C3—68no—
770C22×C3—68no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—84no—
779C22×C3—1216no—
780C22×C3—124no—
781C22×C3D3×#4112yes—
782C22×C3D3×#4112yes—
783C22×C3#100912yes—
784C22×C3C2×C3×#4112yes—
785C22×C3C2×C3×#4112yes—
786C22×C3C3×H(5,𝔽2)12yes—
787C22×C3C24×D311yescharacteristic
788C22×C3C25×C311yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—28no—
794C2×D3—28no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—416no—
799C2×D3—44no—
800C2×D3C2×C3×#4114yes—
801C2×D3C2×C3×#4114yes—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—22no—
814C3×C4—42no—
815C3×C4—42no—
816C3×C4—42no—
817C3×C4—42no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—62no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—62no—
824C3×C4—62no—
825Dic3—22no—
826Dic3—22no—
827Dic3—22no—
828Dic3—22no—
829Dic3—22no—
830C32C2×#55111yescharacteristic, complemented, Sylow
831C23—22no—
832C23—22no—
833C23—22no—
834C23—34no—
835C23—34no—
836C23—32no—
837C23—32no—
838C23—32no—
839C23—68no—
840C23—68no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—124no—
849C23—1216no—
850C23C23×C3×D312yes—
851C23C23×C3×D311yescharacteristic
852Q8—124no—
853D4—68no—
854D4—68no—
855D4—124no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—68no—
868C2×C4—68no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4C23×C3×D312yes—
878C2×C4C23×C3×D312yes—
879C2×C4C23×C3×D312yes—
880C2×C4C23×C3×D312yes—
881C2×C4C23×C3×D312yes—
882C2×C4C23×C3×D312yes—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—24no—
887C2×C3—42no—
888C2×C3—42no—
889C2×C3—64no—
890C2×C3—64no—
891C2×C3—82no—
892C2×C3—122no—
893C2×C3#570514yesdirect product factor
894C2×C3C3×#55114yescomplemented
895C2×C3C2×D3×#4111yescharacteristic
896C2×C3C2×D3×#4111yescharacteristic
897C2×C3C2×#100911yescharacteristic
898C2×C3C22×C3×#4111yescharacteristic
899C2×C3C22×C3×#4111yescharacteristic
900C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
901D3—24no—
902D3—24no—
903D3—42no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—34no—
908C22—34no—
909C22—44no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—68no—
915C22—68no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—1216no—
920C22—124no—
921C22C3×D3×#4112yes—
922C22C3×D3×#4112yes—
923C22C3×#100912yes—
924C22C24×C3×D311yescharacteristic
925C4—22no—
926C4—22no—
927C4—22no—
928C4—22no—
929C4—22no—
930C4—22no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C3—21no—
937C3C2×#570511yescharacteristic, direct product factor
938C3C2×C3×#55111yescharacteristic, complemented
939C2—42no—
940C2—64no—
941C2—64no—
942C2—122no—
943C2C3×#570514yesdirect product factor
944C2C2×C3×D3×#4111yescharacteristic
945C2C2×C3×D3×#4111yescharacteristic
946C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC2×C3×#126D3
hypocenterC3C2×C3×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#126

Complements

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

NH ≅ G/Ntype
1. C2×C32×#126C2semidirect
2. C3×#5705C2direct (N × H)
3. C2×C3×#897C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×#894C2semidirect
6. C2×C3×#894C2semidirect
7. C2×C3×#893C2semidirect
8. C2×C3×#892C2semidirect
9. C2×C3×#885C2semidirect
10. C2×C3×#883C2semidirect
12. C2×C3×D3×C22⋊C4C2semidirect
13. C2×C3×D3×C22⋊C4C2semidirect
14. C2×C3×#879C2semidirect
15. C2×C3×C4×D12C2semidirect
16. C2×C3×#872C2semidirect
18. C2×#5705C3direct (N × H)
27. C22×C3×C4×D3C22semidirect
28. C22×C3×Dic6C22semidirect
29. C32×#126C22semidirect
30. C2×C32×C4⋊C4C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C2×C32×C4⋊C4C22semidirect
36. C2×C32×C42C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C2×C3×C4×Dic3C22semidirect
54. C2×C3×C4×Dic3C22semidirect
55. C3×#897C22semidirect
56. C3×#896C22semidirect
57. C3×#894C22semidirect
58. C3×#894C22semidirect
59. C3×#893C22semidirect
60. C3×#892C22semidirect
61. C3×#885C22semidirect
62. C3×#883C22semidirect
64. C3×D3×C22⋊C4C22semidirect
65. C3×D3×C22⋊C4C22semidirect
66. C3×#879C22semidirect
67. C3×C4×D12C22semidirect
68. C3×#872C22semidirect
72. C2×C3×#126D3semidirect
73. C2×C3×#126C2×C3semidirect
87. #5705C2×C3direct (N × H)
88. C2×#897C2×C3semidirect
89. C2×#896C2×C3semidirect
90. C2×#894C2×C3semidirect
91. C2×#894C2×C3semidirect
92. C2×#893C2×C3semidirect
93. C2×#892C2×C3semidirect
94. C2×#885C2×C3semidirect
95. C2×#883C2×C3semidirect
97. C2×D3×C22⋊C4C2×C3semidirect
98. C2×D3×C22⋊C4C2×C3semidirect
99. C2×#879C2×C3semidirect
100. C2×C4×D12C2×C3semidirect
101. C2×#872C2×C3semidirect
136. C2×C3×C4×D3C23semidirect
138. C2×C3×Dic6C23semidirect
139. C32×C4⋊C4C23semidirect
140. C32×C4⋊C4C23semidirect
141. C32×C4⋊C4C23semidirect
145. C32×C42C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×(C2×D3)⋊C4C23semidirect
156. C3×(C2×D3)⋊C4C23semidirect
157. C3×C4⋊Dic3C23semidirect
158. C3×C4⋊Dic3C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. C3×Dic3⋊C4C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. C3×C4×Dic3C23semidirect
163. C3×C4×Dic3C23semidirect
183. C22×C4×D3C22×C3semidirect
184. C22×Dic6C22×C3semidirect
187. C3×#126C2×D3semidirect
188. C3×#126C22×C3semidirect
208. C2×C3×C4⋊C4C2×D3semidirect
209. C2×C3×C4⋊C4C2×D3semidirect
210. C2×C3×C4⋊C4C2×D3semidirect
211. C2×C3×C4⋊C4C22×C3semidirect
212. C2×C3×C4⋊C4C22×C3semidirect
213. C2×C3×C4⋊C4C22×C3semidirect
239. C2×C3×C42C2×D3semidirect
240. C2×C3×C42C22×C3semidirect
249. C2×(C2×D3)⋊C4C22×C3semidirect
250. C2×(C2×D3)⋊C4C22×C3semidirect
251. C2×(C2×D3)⋊C4C22×C3semidirect
252. C2×C4⋊Dic3C22×C3semidirect
253. C2×C4⋊Dic3C22×C3semidirect
254. C2×Dic3⋊C4C22×C3semidirect
255. C2×Dic3⋊C4C22×C3semidirect
256. C2×Dic3⋊C4C22×C3semidirect
257. C2×C4×Dic3C22×C3semidirect
258. C2×C4×Dic3C22×C3semidirect
259. #897C22×C3semidirect
260. #896C22×C3semidirect
261. #894C22×C3semidirect
262. #894C22×C3semidirect
263. #893C22×C3semidirect
264. #892C22×C3semidirect
265. #885C22×C3semidirect
266. #883C22×C3semidirect
268. D3×C22⋊C4C22×C3semidirect
269. D3×C22⋊C4C22×C3semidirect
270. #879C22×C3semidirect
271. C4×D12C22×C3semidirect
272. #872C22×C3semidirect
327. C2×#126C3×D3semidirect
419. C2×C4×D3C23×C3semidirect
421. C2×Dic6C23×C3semidirect
430. C3×C4⋊C4C22×D3semidirect
431. C3×C4⋊C4C22×D3semidirect
432. C3×C4⋊C4C22×D3semidirect
433. C3×C4⋊C4C23×C3semidirect
434. C3×C4⋊C4C23×C3semidirect
435. C3×C4⋊C4C23×C3semidirect
459. C3×C42C22×D3semidirect
460. C3×C42C23×C3semidirect
469. (C2×D3)⋊C4C23×C3semidirect
470. (C2×D3)⋊C4C23×C3semidirect
471. (C2×D3)⋊C4C23×C3semidirect
472. C4⋊Dic3C23×C3semidirect
473. C4⋊Dic3C23×C3semidirect
474. Dic3⋊C4C23×C3semidirect
475. Dic3⋊C4C23×C3semidirect
476. Dic3⋊C4C23×C3semidirect
477. C4×Dic3C23×C3semidirect
478. C4×Dic3C23×C3semidirect
522. #126C2×C3×D3semidirect
539. C2×C4⋊C4C2×C3×D3semidirect
540. C2×C4⋊C4C2×C3×D3semidirect
541. C2×C4⋊C4C2×C3×D3semidirect
560. C2×C42C2×C3×D3semidirect
683. C2×C32#551semidirect
732. C4⋊C4C22×C3×D3semidirect
733. C4⋊C4C22×C3×D3semidirect
734. C4⋊C4C22×C3×D3semidirect
751. C42C22×C3×D3semidirect
830. C32C2×#551semidirect
893. C2×C3#5705direct (N × H)
894. C2×C3C3×#551semidirect
937. C3C2×#5705direct (N × H)
938. C3C2×C3×#551semidirect
943. C2C3×#5705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C3×#57052
C2×C3×#8972
C2×C3×#8962
C2×C3×#8942
C2×C3×#8932
C2×C3×#8922
C2×C3×#8852
C2×C3×#8832
C2×C3×#8822
C2×C3×D3×C22⋊C42
C2×C3×#8792
C2×C3×C4×D122
C2×C3×#8722
C2×C3×#5513
C2×#57053