Finite Group Databasebeta

← C2×C3×#5620 #11910158

Subgroups — C2×C3×#5620 #11910158

Order 1152.

2901 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×#938C211yesmaximal, characteristic, complemented
6C2×C3×#937C211yesmaximal, characteristic, complemented
7C2×C3×#937C211yesmaximal, characteristic, complemented
8C2×C3×#930C211yesmaximal, characteristic, complemented
9C2×C3×#929C211yesmaximal, characteristic, complemented
10C3×#5620C2116yesmaximal, direct product factor
11C2×C3×#898C211yesmaximal, characteristic, complemented
12C2×C3×#894C211yesmaximal, characteristic, complemented
13C2×C3×#886C211yesmaximal, characteristic, complemented
14C2×C3×#884C211yesmaximal, characteristic, complemented
15C2×C3×#882C211yesmaximal, characteristic, complemented
16C2×C3×#879C211yesmaximal, characteristic, complemented
17C2×C3×#560—31nomaximal
18C2×#5620C311yesmaximal, characteristic, direct product factor
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic, complemented
23C23×C32×C4C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C22×C3×#67C2211yescharacteristic, complemented
30C22×C3×#67C2211yescharacteristic, complemented
31C23×C3×Dic3C2211yescharacteristic, complemented
32C22×C3×D12C2211yescharacteristic
33C22×C3×D12C2211yescharacteristic
34C22×C3×C4×D3C2211yescharacteristic, complemented
35C32×#121C2218yescomplemented
36C2×C32×C4⋊C4C2211yescharacteristic, complemented
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×C32×C22⋊C4C2211yescharacteristic, complemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic, complemented
42C3×#940C2218yescomplemented
43C3×#939C2218yescomplemented
44C3×#939C2218yescomplemented
45C3×#938C2218yescomplemented
46C3×#937C2218yescomplemented
47C3×#937C2218yescomplemented
48C3×#930C2218yescomplemented
49C3×#929C2218yescomplemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic
53C2×C3×(C2×D3)⋊C4C2211yescharacteristic
54C2×C3×(C2×D3)⋊C4C2211yescharacteristic
55C2×C3×(C2×D3)⋊C4C2211yescharacteristic
56C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
57C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
58C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
59C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
60C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
61C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
62C2×C3×C4×Dic3C2211yescharacteristic, complemented
63C3×#898C2218yescomplemented
64C3×#894C2218yescomplemented
65C3×#886C2218yescomplemented
66C3×#884C2218yescomplemented
67C3×#882C2218yescomplemented
68C3×#879C2218yescomplemented
69C3×#560—316no—
70C2×C3×#127—31no—
71C2×C3×#126—31no—
72C2×C3×#126—31no—
73C2×C3×#123—31no—
74C2×C3×#123—31no—
75C2×C3×#123—31no—
76C2×C3×#121—21no—
77C2×C3×#121—31no—
78C2×C3×#121—31no—
79C2×C3×#121—31no—
80C2×C3×#121—31no—
81C2×C3×#121—31no—
82C2×C3×#121D311yescharacteristic, complemented
83C2×C3×#121C2×C311yescharacteristic, complemented
84C2×C3×#120—31no—
85C2×C3×#120—31no—
86C2×C3×#120—31no—
87C2×#940C2×C311yescharacteristic, complemented
88C2×#939C2×C311yescharacteristic, complemented
89C2×#939C2×C311yescharacteristic, complemented
90C2×#938C2×C311yescharacteristic, complemented
91C2×#937C2×C311yescharacteristic, complemented
92C2×#937C2×C311yescharacteristic, complemented
93C2×#930C2×C311yescharacteristic, complemented
94C2×#929C2×C311yescharacteristic, complemented
95#5620C2×C3116yesdirect product factor
96C2×#898C2×C311yescharacteristic, complemented
97C2×#894C2×C311yescharacteristic, complemented
98C2×#886C2×C311yescharacteristic, complemented
99C2×#884C2×C311yescharacteristic, complemented
100C2×#882C2×C311yescharacteristic, complemented
101C2×#879C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C24×C32C2311yescharacteristic
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3—42no—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C2×C32×D4—42no—
113C2×C32×D4—42no—
114C2×C32×D4—42no—
115C2×C32×D4C2314yes—
116C2×C32×D4C2314yes—
117C2×C32×D4C2314yescomplemented
118C22×C32×C4—42no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C22×C32×C4C2314yescomplemented
124C2×C3×#67—42no—
125C2×C3×#67—42no—
126C2×C3×#67—42no—
127C2×C3×#67—42no—
128C2×C3×#67—42no—
129C2×C3×#67—42no—
130C2×C3×#67—42no—
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yes—
134C2×C3×#67C2314yes—
135C2×C3×#67C2314yes—
136C2×C3×#67C2314yescomplemented
137C2×C3×#67C2314yescomplemented
138C22×C3×Dic3—42no—
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C22×C3×Dic3C2311yescharacteristic
144C22×C3×Dic3C2314yescomplemented
145C2×C3×D12—42no—
146C2×C3×D12—42no—
147C2×C3×D12C2314yes—
148C2×C3×D12C2314yes—
149C2×C3×C4×D3—42no—
150C2×C3×C4×D3C2314yescomplemented
151C32×C4⋊C4C2314yescomplemented
152C32×C22⋊C4C2314yes—
153C32×C22⋊C4C2314yescomplemented
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×#217C2314yescomplemented
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2314yescomplemented
164C3×C4⋊Dic3C2314yescomplemented
165C3×C4⋊Dic3C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167C3×Dic3⋊C4C2314yescomplemented
168C3×Dic3⋊C4C2314yescomplemented
169C3×C4×Dic3C2314yescomplemented
170C2×#560—31noSylow
171C25×C3—31no—
172C24×D3C22×C311yescharacteristic
173C22×C3×D4—21no—
174C22×C3×D4—21no—
175C22×C3×D4—21no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4C2×D311yescharacteristic
186C22×C3×D4C2×D311yescharacteristic
187C22×C3×D4C2×D311yescharacteristic, complemented
188C22×C3×D4C22×C311yescharacteristic
189C22×C3×D4C22×C311yescharacteristic
190C22×C3×D4C22×C311yescharacteristic, complemented
191C23×C3×C4—21no—
192C23×C3×C4—31no—
193C23×C3×C4—31no—
194C23×C3×C4C2×D311yescharacteristic, complemented
195C23×C3×C4C22×C311yescharacteristic, complemented
196C22×#67C22×C311yescharacteristic
197C22×#67C22×C311yescharacteristic
198C22×#67C22×C311yescharacteristic
199C22×#67C22×C311yescharacteristic
200C22×#67C22×C311yescharacteristic
201C22×#67C22×C311yescharacteristic, complemented
202C22×#67C22×C311yescharacteristic, complemented
203C23×Dic3C22×C311yescharacteristic, complemented
204C22×D12C22×C311yescharacteristic
205C22×D12C22×C311yescharacteristic
206C22×C4×D3C22×C311yescharacteristic, complemented
207C3×#127—38no—
208C3×#126—38no—
209C3×#126—38no—
210C3×#123—38no—
211C3×#123—38no—
212C3×#123—38no—
213C3×#121—28no—
214C3×#121—38no—
215C3×#121—38no—
216C3×#121—38no—
217C3×#121—38no—
218C3×#121—38no—
219C3×#121C2×D318yescomplemented
220C3×#121C22×C318yescomplemented
221C3×#120—38no—
222C3×#120—38no—
223C3×#120—38no—
224C2×C3×C4⋊C4—21no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
231C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
232C2×C3×C22⋊C4—21no—
233C2×C3×C22⋊C4—21no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—31no—
241C2×C3×C22⋊C4—31no—
242C2×C3×C22⋊C4—31no—
243C2×C3×C22⋊C4—31no—
244C2×C3×C22⋊C4C2×D311yescharacteristic
245C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
246C2×C3×C22⋊C4C22×C311yescharacteristic
247C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
248C2×C3×C42—31no—
249C2×#217C22×C311yescharacteristic
250C2×#217C22×C311yescharacteristic
251C2×#217C22×C311yescharacteristic, complemented
252#940C22×C318yescomplemented
253#939C22×C318yescomplemented
254#939C22×C318yescomplemented
255#938C22×C318yescomplemented
256#937C22×C318yescomplemented
257#937C22×C318yescomplemented
258#930C22×C318yescomplemented
259#929C22×C318yescomplemented
260C2×(C2×D3)⋊C4C22×C311yescharacteristic
261C2×(C2×D3)⋊C4C22×C311yescharacteristic
262C2×(C2×D3)⋊C4C22×C311yescharacteristic
263C2×(C2×D3)⋊C4C22×C311yescharacteristic
264C2×(C2×D3)⋊C4C22×C311yescharacteristic
265C2×(C2×D3)⋊C4C22×C311yescharacteristic
266C2×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
267C2×C4⋊Dic3C22×C311yescharacteristic, complemented
268C2×C4⋊Dic3C22×C311yescharacteristic, complemented
269C2×Dic3⋊C4C22×C311yescharacteristic, complemented
270C2×Dic3⋊C4C22×C311yescharacteristic, complemented
271C2×Dic3⋊C4C22×C311yescharacteristic, complemented
272C2×C4×Dic3C22×C311yescharacteristic, complemented
273#898C22×C318yescomplemented
274#894C22×C318yescomplemented
275#886C22×C318yescomplemented
276#884C22×C318yescomplemented
277#882C22×C318yescomplemented
278#879C22×C318yescomplemented
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32—22no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2412yes—
289C23×C32C2412yes—
290C23×C32C2412yes—
291C23×C32C2411yescharacteristic
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—44no—
304C22×C3×D3—416no—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C32×D4—44no—
309C32×D4—44no—
310C32×D4—44no—
311C2×C32×C4—22no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4—44no—
316C2×C32×C4C2412yes—
317C2×C32×C4C2412yes—
318C2×C32×C4C2412yes—
319C2×C32×C4C2412yes—
320C3×#67—44no—
321C3×#67—44no—
322C3×#67—44no—
323C3×#67—44no—
324C3×#67—44no—
325C3×#67—44no—
326C3×#67—44no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—44no—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C3×D12—44no—
339C3×D12—44no—
340C3×C4×D3—44no—
341#560—316no—
342C2×#127—31no—
343C2×#126—31no—
344C2×#126—31no—
345C2×#123—31no—
346C2×#123—31no—
347C2×#123—31no—
348C2×#121—31no—
349C2×#121—31no—
350C2×#121—31no—
351C2×#121—31no—
352C2×#121—31no—
353C2×#121C3×D311yescharacteristic, complemented
354C2×#120—31no—
355C2×#120—31no—
356C2×#120—31no—
357C24×C3—21no—
358C24×C3—21no—
359C24×C3—21no—
360C24×C3—31no—
361C24×C3—31no—
362C24×C3—31no—
363C24×C3—34no—
364C24×C3—122no—
365C24×C3—122no—
366C24×C3—122no—
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C24×C3C23×C311yescharacteristic
371C24×C3C23×C311yescharacteristic
372C24×C3C23×C311yescharacteristic
373C23×D3—42no—
374C23×D3—42no—
375C23×D3—42no—
376C23×D3C23×C311yescharacteristic
377C23×D3C23×C311yescharacteristic
378C23×D3C23×C311yescharacteristic
379C23×D3C23×C314yes—
380C2×C3×D4—24no—
381C2×C3×D4—24no—
382C2×C3×D4—24no—
383C2×C3×D4—34no—
384C2×C3×D4—34no—
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—34no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—34no—
392C2×C3×D4—42no—
393C2×C3×D4—42no—
394C2×C3×D4—42no—
395C2×C3×D4—42no—
396C2×C3×D4—42no—
397C2×C3×D4—42no—
398C2×C3×D4—44no—
399C2×C3×D4—44no—
400C2×C3×D4—44no—
401C2×C3×D4—122no—
402C2×C3×D4—122no—
403C2×C3×D4—122no—
404C2×C3×D4—122no—
405C2×C3×D4—122no—
406C2×C3×D4—122no—
407C2×C3×D4—122no—
408C2×C3×D4—122no—
409C2×C3×D4—122no—
410C2×C3×D4C22×D314yes—
411C2×C3×D4C22×D314yes—
412C2×C3×D4C22×D314yescomplemented
413C2×C3×D4C23×C314yes—
414C2×C3×D4C23×C314yes—
415C2×C3×D4C23×C314yescomplemented
416C22×C3×C4—21no—
417C22×C3×C4—21no—
418C22×C3×C4—21no—
419C22×C3×C4—21no—
420C22×C3×C4—24no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—34no—
427C22×C3×C4—34no—
428C22×C3×C4—42no—
429C22×C3×C4—42no—
430C22×C3×C4—44no—
431C22×C3×C4—122no—
432C22×C3×C4—122no—
433C22×C3×C4C22×D311yescharacteristic
434C22×C3×C4C22×D311yescharacteristic
435C22×C3×C4C22×D311yescharacteristic
436C22×C3×C4C22×D311yescharacteristic
437C22×C3×C4C22×D314yescomplemented
438C22×C3×C4C23×C311yescharacteristic
439C22×C3×C4C23×C311yescharacteristic
440C22×C3×C4C23×C311yescharacteristic
441C22×C3×C4C23×C311yescharacteristic
442C22×C3×C4C23×C314yescomplemented
443C2×#67—42no—
444C2×#67—42no—
445C2×#67—42no—
446C2×#67—42no—
447C2×#67—42no—
448C2×#67—42no—
449C2×#67—42no—
450C2×#67C23×C314yes—
451C2×#67C23×C314yes—
452C2×#67C23×C314yes—
453C2×#67C23×C314yes—
454C2×#67C23×C314yes—
455C2×#67C23×C314yescomplemented
456C2×#67C23×C314yescomplemented
457C22×Dic3—42no—
458C22×Dic3C23×C311yescharacteristic
459C22×Dic3C23×C311yescharacteristic
460C22×Dic3C23×C311yescharacteristic
461C22×Dic3C23×C311yescharacteristic
462C22×Dic3C23×C311yescharacteristic
463C22×Dic3C23×C314yescomplemented
464C2×D12—42no—
465C2×D12—42no—
466C2×D12C23×C314yes—
467C2×D12C23×C314yes—
468C2×C4×D3—42no—
469C2×C4×D3C23×C314yescomplemented
470C3×C4⋊C4—24no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C4⋊C4—34no—
475C3×C4⋊C4—34no—
476C3×C4⋊C4C22×D314yescomplemented
477C3×C4⋊C4C23×C314yescomplemented
478C3×C22⋊C4—24no—
479C3×C22⋊C4—24no—
480C3×C22⋊C4—34no—
481C3×C22⋊C4—34no—
482C3×C22⋊C4—34no—
483C3×C22⋊C4—34no—
484C3×C22⋊C4—34no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4—34no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4C22×D314yes—
491C3×C22⋊C4C22×D314yescomplemented
492C3×C22⋊C4C23×C314yes—
493C3×C22⋊C4C23×C314yescomplemented
494C3×C42—34no—
495#217C23×C314yes—
496#217C23×C314yes—
497#217C23×C314yescomplemented
498(C2×D3)⋊C4C23×C314yes—
499(C2×D3)⋊C4C23×C314yes—
500(C2×D3)⋊C4C23×C314yes—
501(C2×D3)⋊C4C23×C314yes—
502(C2×D3)⋊C4C23×C314yes—
503(C2×D3)⋊C4C23×C314yes—
504(C2×D3)⋊C4C23×C314yescomplemented
505C4⋊Dic3C23×C314yescomplemented
506C4⋊Dic3C23×C314yescomplemented
507Dic3⋊C4C23×C314yescomplemented
508Dic3⋊C4C23×C314yescomplemented
509Dic3⋊C4C23×C314yescomplemented
510C4×Dic3C23×C314yescomplemented
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—22no—
517C22×C32—22no—
518C22×C32—22no—
519C22×C32—22no—
520C22×C32—44no—
521C22×C32—44no—
522C22×C32—44no—
523C22×C32H(5,𝔽2)12yes—
524C22×C32H(5,𝔽2)12yes—
525C22×C32H(5,𝔽2)12yes—
526C22×C32C2511yescharacteristic
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—416no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539C2×C3×D3—44no—
540C32×C4—22no—
541C32×C4—22no—
542C32×C4—22no—
543C32×C4—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—31no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—31no—
557C22×D4—31no—
558C22×D4—31no—
559C22×D4C2×C3×D311yescharacteristic
560C22×D4C2×C3×D311yescharacteristic
561C22×D4C2×C3×D311yescharacteristic, complemented
562C23×C4—31no—
563C23×C4—31no—
564C23×C4C2×C3×D311yescharacteristic, complemented
565#127—38no—
566#126—38no—
567#126—38no—
568#123—38no—
569#123—38no—
570#123—38no—
571#121—38no—
572#121—38no—
573#121—38no—
574#121—38no—
575#121—38no—
576#121C2×C3×D318yescomplemented
577#120—38no—
578#120—38no—
579#120—38no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—31no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—31no—
584C2×C4⋊C4—31no—
585C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—31no—
591C2×C22⋊C4—31no—
592C2×C22⋊C4—31no—
593C2×C22⋊C4—31no—
594C2×C22⋊C4—31no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4C2×C3×D311yescharacteristic
597C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
598C2×C42—31no—
599C23×C3—24no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—21no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—32no—
623C23×C3—32no—
624C23×C3—32no—
625C23×C3—42no—
626C23×C3—42no—
627C23×C3—42no—
628C23×C3—42no—
629C23×C3—42no—
630C23×C3—42no—
631C23×C3—42no—
632C23×C3—42no—
633C23×C3—62no—
634C23×C3—62no—
635C23×C3—62no—
636C23×C3—62no—
637C23×C3—62no—
638C23×C3—62no—
639C23×C3—62no—
640C23×C3—62no—
641C23×C3—62no—
642C23×C3—124no—
643C23×C3—124no—
644C23×C3—124no—
645C23×C3—1216no—
646C23×C3C23×D312yes—
647C23×C3C23×D312yes—
648C23×C3C23×D312yes—
649C23×C3C23×D311yescharacteristic
650C23×C3C24×C312yes—
651C23×C3C24×C312yes—
652C23×C3C24×C312yes—
653C23×C3C24×C311yescharacteristic
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—44no—
664C22×D3—44no—
665C22×D3—44no—
666C22×D3—416no—
667C22×D3C24×C312yes—
668C22×D3C24×C312yes—
669C22×D3C24×C312yes—
670C3×D4—44no—
671C3×D4—44no—
672C3×D4—44no—
673C3×D4—44no—
674C3×D4—44no—
675C3×D4—44no—
676C3×D4—48no—
677C3×D4—48no—
678C3×D4—48no—
679C3×D4—124no—
680C3×D4—124no—
681C3×D4—124no—
682C3×D4—124no—
683C3×D4—124no—
684C3×D4—124no—
685C3×D4—124no—
686C3×D4—124no—
687C3×D4—124no—
688C2×C3×C4—24no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—22no—
692C2×C3×C4—22no—
693C2×C3×C4—22no—
694C2×C3×C4—22no—
695C2×C3×C4—22no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—32no—
702C2×C3×C4—32no—
703C2×C3×C4—32no—
704C2×C3×C4—32no—
705C2×C3×C4—32no—
706C2×C3×C4—42no—
707C2×C3×C4—42no—
708C2×C3×C4—42no—
709C2×C3×C4—44no—
710C2×C3×C4—44no—
711C2×C3×C4—48no—
712C2×C3×C4—62no—
713C2×C3×C4—62no—
714C2×C3×C4—62no—
715C2×C3×C4—62no—
716C2×C3×C4—62no—
717C2×C3×C4—124no—
718C2×C3×C4—124no—
719C2×C3×C4C23×D312yes—
720C2×C3×C4C23×D312yes—
721C2×C3×C4C23×D312yes—
722C2×C3×C4C23×D312yes—
723C2×C3×C4C24×C312yes—
724C2×C3×C4C24×C312yes—
725C2×C3×C4C24×C312yes—
726C2×C3×C4C24×C312yes—
727#67—44no—
728#67—44no—
729#67—44no—
730#67—44no—
731#67—44no—
732#67—44no—
733#67—44no—
734C2×Dic3—22no—
735C2×Dic3—22no—
736C2×Dic3—22no—
737C2×Dic3—22no—
738C2×Dic3—22no—
739C2×Dic3—44no—
740C2×Dic3C24×C312yes—
741C2×Dic3C24×C312yes—
742C2×Dic3C24×C312yes—
743C2×Dic3C24×C312yes—
744C2×Dic3C24×C312yes—
745D12—44no—
746D12—44no—
747C4×D3—44no—
748C2×C32—42no—
749C2×C32—42no—
750C2×C32—42no—
751C2×C32#56014yescomplemented
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C2×C32C2×H(5,𝔽2)11yescharacteristic
754C2×C32C2×H(5,𝔽2)11yescharacteristic
755C3×D3—42no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—34no—
762C24—122no—
763C24—122no—
764C24—122no—
765C24C22×C3×D311yescharacteristic
766C24C22×C3×D311yescharacteristic
767C24C22×C3×D311yescharacteristic
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—34no—
773C2×D4—34no—
774C2×D4—34no—
775C2×D4—34no—
776C2×D4—34no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—122no—
781C2×D4—122no—
782C2×D4—122no—
783C2×D4—122no—
784C2×D4—122no—
785C2×D4—122no—
786C2×D4—122no—
787C2×D4—122no—
788C2×D4—122no—
789C2×D4C22×C3×D314yes—
790C2×D4C22×C3×D314yes—
791C2×D4C22×C3×D314yescomplemented
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—34no—
798C22×C4—34no—
799C22×C4—42no—
800C22×C4—122no—
801C22×C4—122no—
802C22×C4C22×C3×D311yescharacteristic
803C22×C4C22×C3×D311yescharacteristic
804C22×C4C22×C3×D311yescharacteristic
805C22×C4C22×C3×D311yescharacteristic
806C22×C4C22×C3×D314yescomplemented
807C4⋊C4—34no—
808C4⋊C4—34no—
809C4⋊C4—34no—
810C4⋊C4—34no—
811C4⋊C4—34no—
812C4⋊C4C22×C3×D314yescomplemented
813C22⋊C4—34no—
814C22⋊C4—34no—
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—34no—
818C22⋊C4—34no—
819C22⋊C4—34no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—34no—
823C22⋊C4C22×C3×D314yes—
824C22⋊C4C22×C3×D314yescomplemented
825C42—34no—
826C22×C3—24no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—21no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—48no—
858C22×C3—44no—
859C22×C3—44no—
860C22×C3—44no—
861C22×C3—44no—
862C22×C3—44no—
863C22×C3—44no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—84no—
874C22×C3—84no—
875C22×C3—1216no—
876C22×C3—124no—
877C22×C3—124no—
878C22×C3—124no—
879C22×C3#100412yes—
880C22×C3#100412yes—
881C22×C3#100912yes—
882C22×C3C3×H(5,𝔽2)12yes—
883C22×C3C3×H(5,𝔽2)12yes—
884C22×C3C3×H(5,𝔽2)12yes—
885C22×C3C24×D311yescharacteristic
886C22×C3C25×C311yescharacteristic
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—22no—
896C2×D3—416no—
897C2×D3—44no—
898C2×D3—44no—
899C2×D3—44no—
900C3×C4—24no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—22no—
906C3×C4—22no—
907C3×C4—22no—
908C3×C4—22no—
909C3×C4—42no—
910C3×C4—42no—
911C3×C4—42no—
912C3×C4—62no—
913C3×C4—62no—
914C3×C4—62no—
915C3×C4—62no—
916C3×C4—62no—
917Dic3—22no—
918Dic3—22no—
919Dic3—22no—
920Dic3—22no—
921Dic3—22no—
922C32C2×#56011yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—32no—
933C23—32no—
934C23—32no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—124no—
945C23—124no—
946C23—124no—
947C23—1216no—
948C23C23×C3×D312yes—
949C23C23×C3×D312yes—
950C23C23×C3×D312yes—
951C23C23×C3×D311yescharacteristic
952D4—44no—
953D4—44no—
954D4—44no—
955D4—124no—
956D4—124no—
957D4—124no—
958D4—124no—
959D4—124no—
960D4—124no—
961D4—124no—
962D4—124no—
963D4—124no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—32no—
972C2×C4—32no—
973C2×C4—44no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—62no—
977C2×C4—62no—
978C2×C4—62no—
979C2×C4—124no—
980C2×C4—124no—
981C2×C4C23×C3×D312yes—
982C2×C4C23×C3×D312yes—
983C2×C4C23×C3×D312yes—
984C2×C4C23×C3×D312yes—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—44no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—42no—
994C2×C3—42no—
995C2×C3—42no—
996C2×C3—82no—
997C2×C3—82no—
998C2×C3—122no—
999C2×C3—122no—
1000C2×C3—122no—
1001C2×C3#562014yesdirect product factor
1002C2×C3C3×#56014yescomplemented
1003C2×C3C2×#100411yescharacteristic
1004C2×C3C2×#100411yescharacteristic
1005C2×C3C2×#100911yescharacteristic
1006C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
1007C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
1008C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
1009D3—42no—
1010D3—42no—
1011D3—42no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—1216no—
1034C22—124no—
1035C22—124no—
1036C22—124no—
1037C22C3×#100412yes—
1038C22C3×#100412yes—
1039C22C3×#100912yes—
1040C22C24×C3×D311yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—22no—
1045C4—62no—
1046C4—62no—
1047C4—62no—
1048C4—62no—
1049C4—62no—
1050C3—21no—
1051C3C2×#562011yescharacteristic, direct product factor
1052C3C2×C3×#56011yescharacteristic, complemented
1053C2—42no—
1054C2—42no—
1055C2—42no—
1056C2—122no—
1057C2—122no—
1058C2—122no—
1059C2C3×#562014yesdirect product factor
1060C2C2×C3×#100411yescharacteristic
1061C2C2×C3×#100411yescharacteristic
1062C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#560
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#938C2semidirect
6. C2×C3×#937C2semidirect
7. C2×C3×#937C2semidirect
8. C2×C3×#930C2semidirect
9. C2×C3×#929C2semidirect
10. C3×#5620C2direct (N × H)
11. C2×C3×#898C2semidirect
12. C2×C3×#894C2semidirect
13. C2×C3×#886C2semidirect
14. C2×C3×#884C2semidirect
15. C2×C3×#882C2semidirect
16. C2×C3×#879C2semidirect
18. C2×#5620C3direct (N × H)
22. C22×C32×D4C22semidirect
23. C23×C32×C4C22semidirect
29. C22×C3×#67C22semidirect
30. C22×C3×#67C22semidirect
31. C23×C3×Dic3C22semidirect
34. C22×C3×C4×D3C22semidirect
35. C32×#121C22semidirect
36. C2×C32×C4⋊C4C22semidirect
38. C2×C32×C22⋊C4C22semidirect
41. C2×C3×#217C22semidirect
42. C3×#940C22semidirect
43. C3×#939C22semidirect
44. C3×#939C22semidirect
45. C3×#938C22semidirect
46. C3×#937C22semidirect
47. C3×#937C22semidirect
48. C3×#930C22semidirect
49. C3×#929C22semidirect
56. C2×C3×(C2×D3)⋊C4C22semidirect
57. C2×C3×C4⋊Dic3C22semidirect
58. C2×C3×C4⋊Dic3C22semidirect
59. C2×C3×Dic3⋊C4C22semidirect
60. C2×C3×Dic3⋊C4C22semidirect
61. C2×C3×Dic3⋊C4C22semidirect
62. C2×C3×C4×Dic3C22semidirect
63. C3×#898C22semidirect
64. C3×#894C22semidirect
65. C3×#886C22semidirect
66. C3×#884C22semidirect
67. C3×#882C22semidirect
68. C3×#879C22semidirect
82. C2×C3×#121D3semidirect
83. C2×C3×#121C2×C3semidirect
87. C2×#940C2×C3semidirect
88. C2×#939C2×C3semidirect
89. C2×#939C2×C3semidirect
90. C2×#938C2×C3semidirect
91. C2×#937C2×C3semidirect
92. C2×#937C2×C3semidirect
93. C2×#930C2×C3semidirect
94. C2×#929C2×C3semidirect
95. #5620C2×C3direct (N × H)
96. C2×#898C2×C3semidirect
97. C2×#894C2×C3semidirect
98. C2×#886C2×C3semidirect
99. C2×#884C2×C3semidirect
100. C2×#882C2×C3semidirect
101. C2×#879C2×C3semidirect
117. C2×C32×D4C23semidirect
123. C22×C32×C4C23semidirect
136. C2×C3×#67C23semidirect
137. C2×C3×#67C23semidirect
144. C22×C3×Dic3C23semidirect
150. C2×C3×C4×D3C23semidirect
151. C32×C4⋊C4C23semidirect
153. C32×C22⋊C4C23semidirect
156. C3×#217C23semidirect
163. C3×(C2×D3)⋊C4C23semidirect
164. C3×C4⋊Dic3C23semidirect
165. C3×C4⋊Dic3C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. C3×Dic3⋊C4C23semidirect
168. C3×Dic3⋊C4C23semidirect
169. C3×C4×Dic3C23semidirect
187. C22×C3×D4C2×D3semidirect
190. C22×C3×D4C22×C3semidirect
194. C23×C3×C4C2×D3semidirect
195. C23×C3×C4C22×C3semidirect
201. C22×#67C22×C3semidirect
202. C22×#67C22×C3semidirect
203. C23×Dic3C22×C3semidirect
206. C22×C4×D3C22×C3semidirect
219. C3×#121C2×D3semidirect
220. C3×#121C22×C3semidirect
230. C2×C3×C4⋊C4C2×D3semidirect
231. C2×C3×C4⋊C4C22×C3semidirect
245. C2×C3×C22⋊C4C2×D3semidirect
247. C2×C3×C22⋊C4C22×C3semidirect
251. C2×#217C22×C3semidirect
252. #940C22×C3semidirect
253. #939C22×C3semidirect
254. #939C22×C3semidirect
255. #938C22×C3semidirect
256. #937C22×C3semidirect
257. #937C22×C3semidirect
258. #930C22×C3semidirect
259. #929C22×C3semidirect
266. C2×(C2×D3)⋊C4C22×C3semidirect
267. C2×C4⋊Dic3C22×C3semidirect
268. C2×C4⋊Dic3C22×C3semidirect
269. C2×Dic3⋊C4C22×C3semidirect
270. C2×Dic3⋊C4C22×C3semidirect
271. C2×Dic3⋊C4C22×C3semidirect
272. C2×C4×Dic3C22×C3semidirect
273. #898C22×C3semidirect
274. #894C22×C3semidirect
275. #886C22×C3semidirect
276. #884C22×C3semidirect
277. #882C22×C3semidirect
278. #879C22×C3semidirect
353. C2×#121C3×D3semidirect
412. C2×C3×D4C22×D3semidirect
415. C2×C3×D4C23×C3semidirect
437. C22×C3×C4C22×D3semidirect
442. C22×C3×C4C23×C3semidirect
455. C2×#67C23×C3semidirect
456. C2×#67C23×C3semidirect
463. C22×Dic3C23×C3semidirect
469. C2×C4×D3C23×C3semidirect
476. C3×C4⋊C4C22×D3semidirect
477. C3×C4⋊C4C23×C3semidirect
491. C3×C22⋊C4C22×D3semidirect
493. C3×C22⋊C4C23×C3semidirect
497. #217C23×C3semidirect
504. (C2×D3)⋊C4C23×C3semidirect
505. C4⋊Dic3C23×C3semidirect
506. C4⋊Dic3C23×C3semidirect
507. Dic3⋊C4C23×C3semidirect
508. Dic3⋊C4C23×C3semidirect
509. Dic3⋊C4C23×C3semidirect
510. C4×Dic3C23×C3semidirect
561. C22×D4C2×C3×D3semidirect
564. C23×C4C2×C3×D3semidirect
576. #121C2×C3×D3semidirect
585. C2×C4⋊C4C2×C3×D3semidirect
597. C2×C22⋊C4C2×C3×D3semidirect
751. C2×C32#560semidirect
791. C2×D4C22×C3×D3semidirect
806. C22×C4C22×C3×D3semidirect
812. C4⋊C4C22×C3×D3semidirect
824. C22⋊C4C22×C3×D3semidirect
922. C32C2×#560semidirect
1001. C2×C3#5620direct (N × H)
1002. C2×C3C3×#560semidirect
1051. C3C2×#5620direct (N × H)
1052. C3C2×C3×#560semidirect
1059. C2C3×#5620direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9402
C2×C3×#9392
C2×C3×#9382
C2×C3×#9372
C2×C3×#9302
C2×C3×#9292
C3×#56202
C2×C3×#8982
C2×C3×#8942
C2×C3×#8862
C2×C3×#8842
C2×C3×#8822
C2×C3×#8792
C2×C3×#5603
C2×#56203