Finite Group Databasebeta

← C2×C3×#5615 #11901464

Subgroups — C2×C3×#5615 #11901464

Order 1152.

2733 conjugacy classes of subgroups.

The subgroup lattice has 1008 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×#939C211yesmaximal, characteristic, complemented
6C2×C3×#938C211yesmaximal, characteristic, complemented
7C2×C3×#935C211yesmaximal, characteristic, complemented
8C2×C3×#929C211yesmaximal, characteristic, complemented
9C2×C3×C4×#67C211yesmaximal, characteristic, complemented
10C3×#5615C2116yesmaximal, direct product factor
11C2×C3×#894C211yesmaximal, characteristic, complemented
12C2×C3×#889C211yesmaximal, characteristic, complemented
13C2×C3×#884C211yesmaximal, characteristic, complemented
14C2×C3×#883C211yesmaximal, characteristic, complemented
15C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
16C2×C3×#877C211yesmaximal, characteristic, complemented
17C2×C3×#540—31nomaximal
18C2×#5615C311yesmaximal, characteristic, direct product factor
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C23×C32×C4C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic
27C22×C3×#67C2211yescharacteristic
28C22×C3×#67C2211yescharacteristic
29C23×C3×Dic3C2211yescharacteristic
30C23×C3×Dic3C2211yescharacteristic
31C22×C3×D12C2211yescharacteristic
32C22×C3×C4×D3C2211yescharacteristic
33C22×C3×C4×D3C2211yescharacteristic
34C32×#121C2218yescomplemented
35C2×C32×C4⋊C4C2211yescharacteristic
36C2×C32×C22⋊C4C2211yescharacteristic
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic
42C3×#940C2218yescomplemented
43C3×#939C2218yescomplemented
44C3×#939C2218yescomplemented
45C3×#939C2218yescomplemented
46C3×#938C2218yescomplemented
47C3×#935C2218yescomplemented
48C3×#929C2218yescomplemented
49C3×C4×#67C2218yescomplemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic
53C2×C3×(C2×D3)⋊C4C2211yescharacteristic
54C2×C3×C4⋊Dic3C2211yescharacteristic
55C2×C3×Dic3⋊C4C2211yescharacteristic
56C2×C3×Dic3⋊C4C2211yescharacteristic
57C2×C3×Dic3⋊C4C2211yescharacteristic
58C2×C3×Dic3⋊C4C2211yescharacteristic
59C2×C3×Dic3⋊C4C2211yescharacteristic
60C2×C3×Dic3⋊C4C2211yescharacteristic
61C2×C3×C4×Dic3C2211yescharacteristic
62C2×C3×C4×Dic3C2211yescharacteristic
63C3×#894C2218yescomplemented
64C3×#889C2218yescomplemented
65C3×#884C2218yescomplemented
66C3×#883C2218yescomplemented
67C3×#67⋊C4C2218yescomplemented
68C3×#877C2218yescomplemented
69C3×#540—316no—
70C2×C3×#127—31no—
71C2×C3×#125—31no—
72C2×C3×#123—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×C4×D4—31no—
85C2×C3×C4×D4—31no—
86C2×C3×#117—31no—
87C2×#940C2×C311yescharacteristic, complemented
88C2×#939C2×C311yescharacteristic, complemented
89C2×#939C2×C311yescharacteristic, complemented
90C2×#939C2×C311yescharacteristic, complemented
91C2×#938C2×C311yescharacteristic, complemented
92C2×#935C2×C311yescharacteristic, complemented
93C2×#929C2×C311yescharacteristic, complemented
94C2×C4×#67C2×C311yescharacteristic, complemented
95#5615C2×C3116yesdirect product factor
96C2×#894C2×C311yescharacteristic, complemented
97C2×#889C2×C311yescharacteristic, complemented
98C2×#884C2×C311yescharacteristic, complemented
99C2×#883C2×C311yescharacteristic, complemented
100C2×#67⋊C4C2×C311yescharacteristic, complemented
101C2×#877C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C24×C32C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C2×C32×D4—42no—
108C2×C32×D4—42no—
109C2×C32×D4—42no—
110C2×C32×D4C2314yes—
111C2×C32×D4C2314yes—
112C2×C32×D4C2314yes—
113C22×C32×C4—42no—
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C22×C32×C4C2314yes—
119C2×C3×#67—24no—
120C2×C3×#67—24no—
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67—42no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C22×C3×Dic3—24no—
132C22×C3×Dic3—42no—
133C22×C3×Dic3C2314yes—
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2314yes—
140C22×C3×Dic3C2311yescharacteristic
141C2×C3×D12—42no—
142C2×C3×D12C2314yes—
143C2×C3×C4×D3—42no—
144C2×C3×C4×D3—42no—
145C2×C3×C4×D3C2314yes—
146C2×C3×C4×D3C2314yes—
147C32×C4⋊C4C2314yes—
148C32×C22⋊C4C2314yes—
149C32×C22⋊C4C2314yes—
150C3×#217C2314yes—
151C3×#217C2314yes—
152C3×#217C2314yes—
153C3×#217C2314yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×C4⋊Dic3C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×C4×Dic3C2314yes—
166C3×C4×Dic3C2314yes—
167C2×#540—31noSylow
168C22×C3×D4—21no—
169C22×C3×D4—21no—
170C22×C3×D4—21no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4C2×D311yescharacteristic
179C22×C3×D4C2×D311yescharacteristic
180C22×C3×D4C2×D311yescharacteristic
181C22×C3×D4C22×C311yescharacteristic
182C22×C3×D4C22×C311yescharacteristic
183C22×C3×D4C22×C311yescharacteristic
184C23×C3×C4—21no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C23×C3×C4C2×D311yescharacteristic
190C23×C3×C4C22×C311yescharacteristic
191C22×#67C22×C311yescharacteristic
192C22×#67C22×C311yescharacteristic
193C22×#67C22×C311yescharacteristic
194C22×#67C22×C311yescharacteristic
195C22×#67C22×C311yescharacteristic
196C22×#67C22×C311yescharacteristic
197C23×Dic3C22×C311yescharacteristic
198C23×Dic3C22×C311yescharacteristic
199C22×D12C22×C311yescharacteristic
200C22×C4×D3C22×C311yescharacteristic
201C22×C4×D3C22×C311yescharacteristic
202C3×#127—38no—
203C3×#125—38no—
204C3×#123—38no—
205C3×#123—38no—
206C3×#123—38no—
207C3×#123—38no—
208C3×#121—28no—
209C3×#121—38no—
210C3×#121—38no—
211C3×#121—38no—
212C3×#121—38no—
213C3×#121—38no—
214C3×#121C2×D318yescomplemented
215C3×#121C22×C318yescomplemented
216C3×C4×D4—38no—
217C3×C4×D4—38no—
218C3×#117—38no—
219C2×C3×C4⋊C4—21no—
220C2×C3×C4⋊C4—31no—
221C2×C3×C4⋊C4—31no—
222C2×C3×C4⋊C4—31no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C4⋊C4C2×D311yescharacteristic
228C2×C3×C4⋊C4C22×C311yescharacteristic
229C2×C3×C22⋊C4—21no—
230C2×C3×C22⋊C4—21no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
240C2×C3×C22⋊C4C2×D311yescharacteristic
241C2×C3×C22⋊C4C22×C311yescharacteristic
242C2×C3×C22⋊C4C22×C311yescharacteristic
243C2×C3×C42—31no—
244C2×C3×C42—31no—
245C2×#217C22×C311yescharacteristic
246C2×#217C22×C311yescharacteristic
247C2×#217C22×C311yescharacteristic
248C2×#217C22×C311yescharacteristic
249#940C22×C318yescomplemented
250#939C22×C318yescomplemented
251#939C22×C318yescomplemented
252#939C22×C318yescomplemented
253#938C22×C318yescomplemented
254#935C22×C318yescomplemented
255#929C22×C318yescomplemented
256C4×#67C22×C318yescomplemented
257C2×(C2×D3)⋊C4C22×C311yescharacteristic
258C2×(C2×D3)⋊C4C22×C311yescharacteristic
259C2×(C2×D3)⋊C4C22×C311yescharacteristic
260C2×(C2×D3)⋊C4C22×C311yescharacteristic
261C2×C4⋊Dic3C22×C311yescharacteristic
262C2×Dic3⋊C4C22×C311yescharacteristic
263C2×Dic3⋊C4C22×C311yescharacteristic
264C2×Dic3⋊C4C22×C311yescharacteristic
265C2×Dic3⋊C4C22×C311yescharacteristic
266C2×Dic3⋊C4C22×C311yescharacteristic
267C2×Dic3⋊C4C22×C311yescharacteristic
268C2×C4×Dic3C22×C311yescharacteristic
269C2×C4×Dic3C22×C311yescharacteristic
270#894C22×C318yescomplemented
271#889C22×C318yescomplemented
272#884C22×C318yescomplemented
273#883C22×C318yescomplemented
274#67⋊C4C22×C318yescomplemented
275#877C22×C318yescomplemented
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32—22no—
283C23×C32—22no—
284C23×C32—22no—
285C23×C32C2412yes—
286C23×C32C2412yes—
287C23×C32C2412yes—
288C23×C32C2411yescharacteristic
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C32×D4—44no—
298C32×D4—44no—
299C32×D4—44no—
300C2×C32×C4—22no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4—44no—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C32×C4C2412yes—
308C2×C32×C4C2412yes—
309C3×#67—28no—
310C3×#67—28no—
311C3×#67—44no—
312C3×#67—44no—
313C3×#67—44no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—28no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3#4114yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C3×D12—44no—
330C3×C4×D3—44no—
331C3×C4×D3—44no—
332#540—316no—
333C2×#127—31no—
334C2×#125—31no—
335C2×#123—31no—
336C2×#123—31no—
337C2×#123—31no—
338C2×#123—31no—
339C2×#121—31no—
340C2×#121—31no—
341C2×#121—31no—
342C2×#121—31no—
343C2×#121—31no—
344C2×#121C3×D311yescharacteristic, complemented
345C2×C4×D4—31no—
346C2×C4×D4—31no—
347C2×#117—31no—
348C24×C3—21no—
349C24×C3—21no—
350C24×C3—21no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C24×C3C23×C311yescharacteristic
357C24×C3C23×C311yescharacteristic
358C24×C3C23×C311yescharacteristic
359C23×D3C23×C311yescharacteristic
360C23×D3C23×C311yescharacteristic
361C2×C3×D4—24no—
362C2×C3×D4—24no—
363C2×C3×D4—24no—
364C2×C3×D4—34no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—42no—
372C2×C3×D4—42no—
373C2×C3×D4—42no—
374C2×C3×D4—42no—
375C2×C3×D4—42no—
376C2×C3×D4—42no—
377C2×C3×D4—44no—
378C2×C3×D4—44no—
379C2×C3×D4—44no—
380C2×C3×D4—64no—
381C2×C3×D4—64no—
382C2×C3×D4—122no—
383C2×C3×D4—122no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C2×C3×D4—122no—
387C2×C3×D4C22×D314yes—
388C2×C3×D4C22×D314yes—
389C2×C3×D4C22×D314yes—
390C2×C3×D4C23×C314yes—
391C2×C3×D4C23×C314yes—
392C2×C3×D4C23×C314yes—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—24no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—34no—
406C22×C3×C4—34no—
407C22×C3×C4—34no—
408C22×C3×C4—42no—
409C22×C3×C4—42no—
410C22×C3×C4—44no—
411C22×C3×C4—64no—
412C22×C3×C4—122no—
413C22×C3×C4—122no—
414C22×C3×C4—122no—
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C22×C3×C4C22×D311yescharacteristic
418C22×C3×C4C22×D311yescharacteristic
419C22×C3×C4C22×D314yes—
420C22×C3×C4C23×C311yescharacteristic
421C22×C3×C4C23×C311yescharacteristic
422C22×C3×C4C23×C311yescharacteristic
423C22×C3×C4C23×C311yescharacteristic
424C22×C3×C4C23×C314yes—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—42no—
428C2×#67—42no—
429C2×#67—42no—
430C2×#67—42no—
431C2×#67C23×C314yes—
432C2×#67C23×C314yes—
433C2×#67C23×C314yes—
434C2×#67C23×C314yes—
435C2×#67C23×C314yes—
436C2×#67C23×C314yes—
437C22×Dic3—24no—
438C22×Dic3—42no—
439C22×Dic3C23×C314yes—
440C22×Dic3C23×C311yescharacteristic
441C22×Dic3C23×C311yescharacteristic
442C22×Dic3C23×C311yescharacteristic
443C22×Dic3C23×C311yescharacteristic
444C22×Dic3C23×C311yescharacteristic
445C22×Dic3C23×C314yes—
446C22×Dic3C23×C311yescharacteristic
447C2×D12—42no—
448C2×D12C23×C314yes—
449C2×C4×D3—42no—
450C2×C4×D3—42no—
451C2×C4×D3C23×C314yes—
452C2×C4×D3C23×C314yes—
453C3×C4⋊C4—24no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4—34no—
460C3×C4⋊C4—34no—
461C3×C4⋊C4C22×D314yes—
462C3×C4⋊C4C23×C314yes—
463C3×C22⋊C4—24no—
464C3×C22⋊C4—24no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4C22×D314yes—
474C3×C22⋊C4C22×D314yes—
475C3×C22⋊C4C23×C314yes—
476C3×C22⋊C4C23×C314yes—
477C3×C42—34no—
478C3×C42—34no—
479#217C23×C314yes—
480#217C23×C314yes—
481#217C23×C314yes—
482#217C23×C314yes—
483(C2×D3)⋊C4C23×C314yes—
484(C2×D3)⋊C4C23×C314yes—
485(C2×D3)⋊C4C23×C314yes—
486(C2×D3)⋊C4C23×C314yes—
487C4⋊Dic3C23×C314yes—
488Dic3⋊C4C23×C314yes—
489Dic3⋊C4C23×C314yes—
490Dic3⋊C4C23×C314yes—
491Dic3⋊C4C23×C314yes—
492Dic3⋊C4C23×C314yes—
493Dic3⋊C4C23×C314yes—
494C4×Dic3C23×C314yes—
495C4×Dic3C23×C314yes—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32—44no—
506C22×C32—44no—
507C22×C32—44no—
508C22×C32C2×#4112yes—
509C22×C32H(5,𝔽2)12yes—
510C22×C32H(5,𝔽2)12yes—
511C22×C32C2511yescharacteristic
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3C2×#4114yes—
530C22×D4—31no—
531C22×D4—31no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4C2×C3×D311yescharacteristic
538C22×D4C2×C3×D311yescharacteristic
539C22×D4C2×C3×D311yescharacteristic
540C23×C4—31no—
541C23×C4—31no—
542C23×C4—31no—
543C23×C4—31no—
544C23×C4C2×C3×D311yescharacteristic
545#127—38no—
546#125—38no—
547#123—38no—
548#123—38no—
549#123—38no—
550#123—38no—
551#121—38no—
552#121—38no—
553#121—38no—
554#121—38no—
555#121—38no—
556#121C2×C3×D318yescomplemented
557C4×D4—38no—
558C4×D4—38no—
559#117—38no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—31no—
567C2×C4⋊C4C2×C3×D311yescharacteristic
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4C2×C3×D311yescharacteristic
577C2×C22⋊C4C2×C3×D311yescharacteristic
578C2×C42—31no—
579C2×C42—31no—
580C23×C3—24no—
581C23×C3—22no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—32no—
604C23×C3—32no—
605C23×C3—42no—
606C23×C3—42no—
607C23×C3—42no—
608C23×C3—42no—
609C23×C3—42no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—42no—
613C23×C3—62no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3C23×D312yes—
620C23×C3C23×D312yes—
621C23×C3C23×D312yes—
622C23×C3C23×D311yescharacteristic
623C23×C3C24×C312yes—
624C23×C3C24×C312yes—
625C23×C3C24×C312yes—
626C23×C3C24×C311yescharacteristic
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3C24×C312yes—
634C22×D3C24×C312yes—
635C3×D4—44no—
636C3×D4—44no—
637C3×D4—44no—
638C3×D4—44no—
639C3×D4—44no—
640C3×D4—44no—
641C3×D4—48no—
642C3×D4—48no—
643C3×D4—48no—
644C3×D4—68no—
645C3×D4—68no—
646C3×D4—124no—
647C3×D4—124no—
648C3×D4—124no—
649C3×D4—124no—
650C3×D4—124no—
651C2×C3×C4—24no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—22no—
664C2×C3×C4—34no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—42no—
672C2×C3×C4—42no—
673C2×C3×C4—42no—
674C2×C3×C4—44no—
675C2×C3×C4—44no—
676C2×C3×C4—48no—
677C2×C3×C4—68no—
678C2×C3×C4—62no—
679C2×C3×C4—62no—
680C2×C3×C4—62no—
681C2×C3×C4—62no—
682C2×C3×C4—62no—
683C2×C3×C4—124no—
684C2×C3×C4—124no—
685C2×C3×C4—124no—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D312yes—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C24×C312yes—
691C2×C3×C4C24×C312yes—
692C2×C3×C4C24×C312yes—
693C2×C3×C4C24×C312yes—
694#67—28no—
695#67—28no—
696#67—44no—
697#67—44no—
698#67—44no—
699#67—44no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—28no—
706C2×Dic3—44no—
707C2×Dic3C3×#4114yes—
708C2×Dic3C24×C312yes—
709C2×Dic3C24×C312yes—
710C2×Dic3C24×C312yes—
711C2×Dic3C24×C312yes—
712C2×Dic3C24×C312yes—
713C2×Dic3C24×C312yes—
714D12—44no—
715C4×D3—44no—
716C4×D3—44no—
717C2×C32—42no—
718C2×C32—42no—
719C2×C32—42no—
720C2×C32#54014yescomplemented
721C2×C32C22×#4111yescharacteristic
722C2×C32C2×H(5,𝔽2)11yescharacteristic
723C2×C32C2×H(5,𝔽2)11yescharacteristic
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24C22×C3×D311yescharacteristic
729C24C22×C3×D311yescharacteristic
730C24C22×C3×D311yescharacteristic
731C2×D4—34no—
732C2×D4—34no—
733C2×D4—34no—
734C2×D4—34no—
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—34no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—64no—
742C2×D4—64no—
743C2×D4—122no—
744C2×D4—122no—
745C2×D4—122no—
746C2×D4—122no—
747C2×D4—122no—
748C2×D4C22×C3×D314yes—
749C2×D4C22×C3×D314yes—
750C2×D4C22×C3×D314yes—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—34no—
758C22×C4—34no—
759C22×C4—34no—
760C22×C4—34no—
761C22×C4—42no—
762C22×C4—64no—
763C22×C4—122no—
764C22×C4—122no—
765C22×C4—122no—
766C22×C4C22×C3×D311yescharacteristic
767C22×C4C22×C3×D311yescharacteristic
768C22×C4C22×C3×D311yescharacteristic
769C22×C4C22×C3×D311yescharacteristic
770C22×C4C22×C3×D314yes—
771C4⋊C4—34no—
772C4⋊C4—34no—
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—34no—
776C4⋊C4—34no—
777C4⋊C4—34no—
778C4⋊C4C22×C3×D314yes—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4C22×C3×D314yes—
788C22⋊C4C22×C3×D314yes—
789C42—34no—
790C42—34no—
791C22×C3—24no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—21no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—48no—
823C22×C3—44no—
824C22×C3—44no—
825C22×C3—44no—
826C22×C3—44no—
827C22×C3—44no—
828C22×C3—44no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—84no—
836C22×C3—84no—
837C22×C3—124no—
838C22×C3—124no—
839C22×C3#100412yes—
840C22×C3#100412yes—
841C22×C3D3×#4112yes—
842C22×C3C2×C3×#4112yes—
843C22×C3C3×H(5,𝔽2)12yes—
844C22×C3C3×H(5,𝔽2)12yes—
845C22×C3C24×D311yescharacteristic
846C22×C3C25×C311yescharacteristic
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—44no—
854C2×D3—44no—
855C3×C4—24no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—34no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—22no—
878Dic3C2×C3×#4114yes—
879C32C2×#54011yescharacteristic, complemented, Sylow
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—32no—
890C23—32no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23C23×C3×D312yes—
898C23C23×C3×D312yes—
899C23C23×C3×D312yes—
900C23C23×C3×D311yescharacteristic
901D4—44no—
902D4—44no—
903D4—44no—
904D4—68no—
905D4—68no—
906D4—124no—
907D4—124no—
908D4—124no—
909D4—124no—
910D4—124no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—34no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—44no—
923C2×C4—68no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—124no—
930C2×C4—124no—
931C2×C4—124no—
932C2×C4C23×C3×D312yes—
933C2×C4C23×C3×D312yes—
934C2×C4C23×C3×D312yes—
935C2×C4C23×C3×D312yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—24no—
940C2×C3—44no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—42no—
946C2×C3—42no—
947C2×C3—82no—
948C2×C3—82no—
949C2×C3—122no—
950C2×C3—122no—
951C2×C3#561514yesdirect product factor
952C2×C3C3×#54014yescomplemented
953C2×C3C2×#100411yescharacteristic
954C2×C3C2×#100411yescharacteristic
955C2×C3C2×D3×#4111yescharacteristic
956C2×C3C22×C3×#4111yescharacteristic
957C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
958C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
959D3—42no—
960D3—42no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—124no—
980C22—124no—
981C22C3×#100412yes—
982C22C3×#100412yes—
983C22C3×D3×#4112yes—
984C22C24×C3×D311yescharacteristic
985C4—22no—
986C4—22no—
987C4—22no—
988C4—22no—
989C4—34no—
990C4—62no—
991C4—62no—
992C4—62no—
993C4—62no—
994C4—62no—
995C3—21no—
996C3C2×#561511yescharacteristic, direct product factor
997C3C2×C3×#54011yescharacteristic, complemented
998C2—42no—
999C2—42no—
1000C2—42no—
1001C2—122no—
1002C2—122no—
1003C2C3×#561514yesdirect product factor
1004C2C2×C3×#100411yescharacteristic
1005C2C2×C3×#100411yescharacteristic
1006C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#540
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×#939C2semidirect
6. C2×C3×#938C2semidirect
7. C2×C3×#935C2semidirect
8. C2×C3×#929C2semidirect
9. C2×C3×C4×#67C2semidirect
10. C3×#5615C2direct (N × H)
11. C2×C3×#894C2semidirect
12. C2×C3×#889C2semidirect
13. C2×C3×#884C2semidirect
14. C2×C3×#883C2semidirect
15. C2×C3×#67⋊C4C2semidirect
16. C2×C3×#877C2semidirect
18. C2×#5615C3direct (N × H)
34. C32×#121C22semidirect
42. C3×#940C22semidirect
43. C3×#939C22semidirect
44. C3×#939C22semidirect
45. C3×#939C22semidirect
46. C3×#938C22semidirect
47. C3×#935C22semidirect
48. C3×#929C22semidirect
49. C3×C4×#67C22semidirect
63. C3×#894C22semidirect
64. C3×#889C22semidirect
65. C3×#884C22semidirect
66. C3×#883C22semidirect
67. C3×#67⋊C4C22semidirect
68. C3×#877C22semidirect
82. C2×C3×#121D3semidirect
83. C2×C3×#121C2×C3semidirect
87. C2×#940C2×C3semidirect
88. C2×#939C2×C3semidirect
89. C2×#939C2×C3semidirect
90. C2×#939C2×C3semidirect
91. C2×#938C2×C3semidirect
92. C2×#935C2×C3semidirect
93. C2×#929C2×C3semidirect
94. C2×C4×#67C2×C3semidirect
95. #5615C2×C3direct (N × H)
96. C2×#894C2×C3semidirect
97. C2×#889C2×C3semidirect
98. C2×#884C2×C3semidirect
99. C2×#883C2×C3semidirect
100. C2×#67⋊C4C2×C3semidirect
101. C2×#877C2×C3semidirect
214. C3×#121C2×D3semidirect
215. C3×#121C22×C3semidirect
249. #940C22×C3semidirect
250. #939C22×C3semidirect
251. #939C22×C3semidirect
252. #939C22×C3semidirect
253. #938C22×C3semidirect
254. #935C22×C3semidirect
255. #929C22×C3semidirect
256. C4×#67C22×C3semidirect
270. #894C22×C3semidirect
271. #889C22×C3semidirect
272. #884C22×C3semidirect
273. #883C22×C3semidirect
274. #67⋊C4C22×C3semidirect
275. #877C22×C3semidirect
344. C2×#121C3×D3semidirect
556. #121C2×C3×D3semidirect
720. C2×C32#540semidirect
879. C32C2×#540semidirect
951. C2×C3#5615direct (N × H)
952. C2×C3C3×#540semidirect
996. C3C2×#5615direct (N × H)
997. C3C2×C3×#540semidirect
1003. C2C3×#5615direct (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×#9352
C2×C3×#9292
C2×C3×C4×#672
C3×#56152
C2×C3×#8942
C2×C3×#8892
C2×C3×#8842
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×#8772
C2×C3×#5403
C2×#56153