Finite Group Databasebeta

← C2×C3×#5710 #11901616

Subgroups — C2×C3×#5710 #11901616

Order 1152.

2387 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C3×#5710C2116yesmaximal, direct product factor
3C2×C3×#898C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#896C211yesmaximal, characteristic, complemented
6C2×C3×#894C211yesmaximal, characteristic, complemented
7C2×C3×#892C211yesmaximal, characteristic, complemented
8C2×C3×#888C211yesmaximal, characteristic, complemented
9C2×C3×#886C211yesmaximal, characteristic, complemented
10C2×C3×#885C211yesmaximal, characteristic, complemented
11C2×C3×#885C211yesmaximal, characteristic, complemented
12C2×C3×#884C211yesmaximal, characteristic
13C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
14C2×C3×#878C211yesmaximal, characteristic, complemented
15C2×C3×#875C211yesmaximal, characteristic, complemented
16C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
17C2×C3×#542—31nomaximal
18C2×#5710C311yesmaximal, characteristic, direct product factor
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C32×#126C2218yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×C32×C42C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
46C2×C3×C4⋊Dic3C2211yescharacteristic
47C2×C3×C4⋊Dic3C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C2×C3×C4×Dic3C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55C3×#898C2218yescomplemented
56C3×#897C2218yescomplemented
57C3×#896C2218yescomplemented
58C3×#894C2218yescomplemented
59C3×#892C2218yescomplemented
60C3×#888C2218yescomplemented
61C3×#886C2218yescomplemented
62C3×#885C2218yescomplemented
63C3×#885C2218yescomplemented
64C3×#884C2218yes—
65C3×#67⋊C4C2218yescomplemented
66C3×#878C2218yescomplemented
67C3×#875C2218yescomplemented
68C3×C4×Dic6C2218yescomplemented
69C3×#542—316no—
70C2×C3×C4⋊Q8—31no—
71C2×C3×#126—21no—
72C2×C3×#126—31no—
73C2×C3×#126D311yescharacteristic, complemented
74C2×C3×#126C2×C311yescharacteristic, complemented
75C2×C3×#124—31no—
76C2×C3×#124—31no—
77C2×C3×#124—31no—
78C2×C3×#123—31no—
79C2×C3×#123—31no—
80C2×C3×C22⋊Q8—31no—
81C2×C3×C22⋊Q8—31no—
82C2×C3×C22⋊Q8—31no—
83C2×C3×#121—31no—
84C2×C3×C4×Q8—31no—
85C2×C3×C4×D4—31no—
86C2×C3×#117—31no—
87#5710C2×C3116yesdirect product factor
88C2×#898C2×C311yescharacteristic, complemented
89C2×#897C2×C311yescharacteristic, complemented
90C2×#896C2×C311yescharacteristic, complemented
91C2×#894C2×C311yescharacteristic, complemented
92C2×#892C2×C311yescharacteristic, complemented
93C2×#888C2×C311yescharacteristic, complemented
94C2×#886C2×C311yescharacteristic, complemented
95C2×#885C2×C311yescharacteristic, complemented
96C2×#885C2×C311yescharacteristic, complemented
97C2×#884C2×C311yescharacteristic
98C2×#67⋊C4C2×C311yescharacteristic, complemented
99C2×#878C2×C311yescharacteristic, complemented
100C2×#875C2×C311yescharacteristic, complemented
101C2×C4×Dic6C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C2×C3×#67—24no—
112C2×C3×#67—42no—
113C2×C3×#67C2314yes—
114C2×C3×#67C2314yes—
115C22×C3×Dic3—42no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2314yes—
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—42no—
124C2×C3×D12C2314yes—
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3—42no—
127C2×C3×C4×D3C2314yes—
128C2×C3×C4×D3C2314yes—
129C2×C3×Dic6—24no—
130C2×C3×Dic6—42no—
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2314yes—
134C2×C3×Dic6C2314yes—
135C32×C4⋊C4C2314yes—
136C32×C4⋊C4C2314yes—
137C32×C4⋊C4C2314yes—
138C32×C22⋊C4C2314yes—
139C32×C22⋊C4C2314yes—
140C32×C22⋊C4C2314yes—
141C32×C42C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161C2×#542—31noSylow
162C22×C3×Q8—31no—
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C22×#67C22×C311yescharacteristic
172C22×#67C22×C311yescharacteristic
173C23×Dic3C22×C311yescharacteristic
174C22×D12C22×C311yescharacteristic
175C22×C4×D3C22×C311yescharacteristic
176C22×C4×D3C22×C311yescharacteristic
177C22×Dic6C22×C311yescharacteristic
178C22×Dic6C22×C311yescharacteristic
179C22×Dic6C22×C311yescharacteristic
180C3×C4⋊Q8—38no—
181C3×#126—28no—
182C3×#126—38no—
183C3×#126C2×D318yescomplemented
184C3×#126C22×C318yescomplemented
185C3×#124—38no—
186C3×#124—38no—
187C3×#124—38no—
188C3×#123—38no—
189C3×#123—38no—
190C3×C22⋊Q8—38no—
191C3×C22⋊Q8—38no—
192C3×C22⋊Q8—38no—
193C3×#121—38no—
194C3×C4×Q8—38no—
195C3×C4×D4—38no—
196C3×#117—38no—
197C2×C3×C4⋊C4—21no—
198C2×C3×C4⋊C4—21no—
199C2×C3×C4⋊C4—21no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4C2×D311yescharacteristic
208C2×C3×C4⋊C4C2×D311yescharacteristic
209C2×C3×C4⋊C4C2×D311yescharacteristic
210C2×C3×C4⋊C4C22×C311yescharacteristic
211C2×C3×C4⋊C4C22×C311yescharacteristic
212C2×C3×C4⋊C4C22×C311yescharacteristic
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—21no—
215C2×C3×C22⋊C4—21no—
216C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
226C2×C3×C22⋊C4C2×D311yescharacteristic
227C2×C3×C22⋊C4C2×D311yescharacteristic
228C2×C3×C22⋊C4C22×C311yescharacteristic
229C2×C3×C22⋊C4C22×C311yescharacteristic
230C2×C3×C22⋊C4C22×C311yescharacteristic
231C2×C3×C42—21no—
232C2×C3×C42—31no—
233C2×C3×C42—31no—
234C2×C3×C42—31no—
235C2×C3×C42C2×D311yescharacteristic
236C2×C3×C42C22×C311yescharacteristic
237C2×#217C22×C311yescharacteristic
238C2×(C2×D3)⋊C4C22×C311yescharacteristic
239C2×(C2×D3)⋊C4C22×C311yescharacteristic
240C2×(C2×D3)⋊C4C22×C311yescharacteristic
241C2×(C2×D3)⋊C4C22×C311yescharacteristic
242C2×(C2×D3)⋊C4C22×C311yescharacteristic
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×(C2×D3)⋊C4C22×C311yescharacteristic
245C2×(C2×D3)⋊C4C22×C311yescharacteristic
246C2×C4⋊Dic3C22×C311yescharacteristic
247C2×C4⋊Dic3C22×C311yescharacteristic
248C2×C4⋊Dic3C22×C311yescharacteristic
249C2×Dic3⋊C4C22×C311yescharacteristic
250C2×Dic3⋊C4C22×C311yescharacteristic
251C2×Dic3⋊C4C22×C311yescharacteristic
252C2×Dic3⋊C4C22×C311yescharacteristic
253C2×C4×Dic3C22×C311yescharacteristic
254C2×C4×Dic3C22×C311yescharacteristic
255C2×C4×Dic3C22×C311yescharacteristic
256#898C22×C318yescomplemented
257#897C22×C318yescomplemented
258#896C22×C318yescomplemented
259#894C22×C318yescomplemented
260#892C22×C318yescomplemented
261#888C22×C318yescomplemented
262#886C22×C318yescomplemented
263#885C22×C318yescomplemented
264#885C22×C318yescomplemented
265#884C22×C318yes—
266#67⋊C4C22×C318yescomplemented
267#878C22×C318yescomplemented
268#875C22×C318yescomplemented
269C4×Dic6C22×C318yescomplemented
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4—22no—
287C2×C32×C4—22no—
288C2×C32×C4—22no—
289C2×C32×C4C2412yes—
290C2×C32×C4C2412yes—
291C2×C32×C4C2412yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C3×#67—28no—
296C3×#67—44no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—44no—
303C2×C3×Dic3#4114yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C3×D12—44no—
311C3×C4×D3—28no—
312C3×C4×D3—44no—
313C3×Dic6—28no—
314C3×Dic6—44no—
315C3×Dic6—44no—
316#542—316no—
317C2×C4⋊Q8—31no—
318C2×#126—31no—
319C2×#126C3×D311yescharacteristic, complemented
320C2×#124—31no—
321C2×#124—31no—
322C2×#124—31no—
323C2×#123—31no—
324C2×#123—31no—
325C2×C22⋊Q8—31no—
326C2×C22⋊Q8—31no—
327C2×C22⋊Q8—31no—
328C2×#121—31no—
329C2×C4×Q8—31no—
330C2×C4×D4—31no—
331C2×#117—31no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C23×C311yescharacteristic
337C23×D3C23×C311yescharacteristic
338C23×D3C23×C311yescharacteristic
339C2×C3×Q8—34no—
340C2×C3×Q8—34no—
341C2×C3×Q8—34no—
342C2×C3×Q8—64no—
343C2×C3×Q8—122no—
344C2×C3×Q8—122no—
345C2×C3×D4—34no—
346C2×C3×D4—34no—
347C2×C3×D4—34no—
348C2×C3×D4—64no—
349C2×C3×D4—122no—
350C2×C3×D4—122no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—34no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4—64no—
367C22×C3×C4—122no—
368C22×C3×C4—122no—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C23×C311yescharacteristic
376C22×C3×C4C23×C311yescharacteristic
377C22×C3×C4C23×C311yescharacteristic
378C22×C3×C4C23×C311yescharacteristic
379C22×C3×C4C23×C311yescharacteristic
380C22×C3×C4C23×C311yescharacteristic
381C2×#67—24no—
382C2×#67—42no—
383C2×#67C23×C314yes—
384C2×#67C23×C314yes—
385C22×Dic3—42no—
386C22×Dic3C23×C311yescharacteristic
387C22×Dic3C23×C311yescharacteristic
388C22×Dic3C23×C311yescharacteristic
389C22×Dic3C23×C311yescharacteristic
390C22×Dic3C23×C311yescharacteristic
391C22×Dic3C23×C314yes—
392C22×Dic3C23×C311yescharacteristic
393C2×D12—42no—
394C2×D12C23×C314yes—
395C2×C4×D3—24no—
396C2×C4×D3—42no—
397C2×C4×D3C23×C314yes—
398C2×C4×D3C23×C314yes—
399C2×Dic6—24no—
400C2×Dic6—42no—
401C2×Dic6—42no—
402C2×Dic6C23×C314yes—
403C2×Dic6C23×C314yes—
404C2×Dic6C23×C314yes—
405C3×C4⋊C4—24no—
406C3×C4⋊C4—24no—
407C3×C4⋊C4—24no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4C22×D314yes—
416C3×C4⋊C4C22×D314yes—
417C3×C4⋊C4C22×D314yes—
418C3×C4⋊C4C23×C314yes—
419C3×C4⋊C4C23×C314yes—
420C3×C4⋊C4C23×C314yes—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—24no—
423C3×C22⋊C4—24no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4C22×D314yes—
434C3×C22⋊C4C22×D314yes—
435C3×C22⋊C4C22×D314yes—
436C3×C22⋊C4C23×C314yes—
437C3×C22⋊C4C23×C314yes—
438C3×C22⋊C4C23×C314yes—
439C3×C42—24no—
440C3×C42—34no—
441C3×C42—34no—
442C3×C42—34no—
443C3×C42C22×D314yes—
444C3×C42C23×C314yes—
445#217C23×C314yes—
446(C2×D3)⋊C4C23×C314yes—
447(C2×D3)⋊C4C23×C314yes—
448(C2×D3)⋊C4C23×C314yes—
449(C2×D3)⋊C4C23×C314yes—
450(C2×D3)⋊C4C23×C314yes—
451(C2×D3)⋊C4C23×C314yes—
452(C2×D3)⋊C4C23×C314yes—
453(C2×D3)⋊C4C23×C314yes—
454C4⋊Dic3C23×C314yes—
455C4⋊Dic3C23×C314yes—
456C4⋊Dic3C23×C314yes—
457Dic3⋊C4C23×C314yes—
458Dic3⋊C4C23×C314yes—
459Dic3⋊C4C23×C314yes—
460Dic3⋊C4C23×C314yes—
461C4×Dic3C23×C314yes—
462C4×Dic3C23×C314yes—
463C4×Dic3C23×C314yes—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—44no—
468C22×C32C2×#4112yes—
469C22×C32H(5,𝔽2)12yes—
470C22×C322−1+412yes—
471C22×C32C2511yescharacteristic
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—44no—
479C2×C3×D3—44no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3C2×#4114yes—
492C22×Q8—31no—
493C22×Q8—31no—
494C22×Q8—31no—
495C22×D4—31no—
496C22×D4—31no—
497C22×D4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—31no—
501C4⋊Q8—38no—
502#126—38no—
503#126C2×C3×D318yescomplemented
504#124—38no—
505#124—38no—
506#124—38no—
507#123—38no—
508#123—38no—
509C22⋊Q8—38no—
510C22⋊Q8—38no—
511C22⋊Q8—38no—
512#121—38no—
513C4×Q8—38no—
514C4×D4—38no—
515#117—38no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4C2×C3×D311yescharacteristic
524C2×C4⋊C4C2×C3×D311yescharacteristic
525C2×C4⋊C4C2×C3×D311yescharacteristic
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4C2×C3×D311yescharacteristic
536C2×C22⋊C4C2×C3×D311yescharacteristic
537C2×C22⋊C4C2×C3×D311yescharacteristic
538C2×C42—31no—
539C2×C42—31no—
540C2×C42—31no—
541C2×C42C2×C3×D311yescharacteristic
542C23×C3—22no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—21no—
549C23×C3—22no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3C23×D312yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C24×C312yes—
564C23×C3C24×C311yescharacteristic
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3C24×C312yes—
572C22×D3C24×C312yes—
573C3×Q8—68no—
574C3×Q8—124no—
575C3×Q8—124no—
576C3×D4—68no—
577C3×D4—124no—
578C3×D4—124no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—34no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—42no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—42no—
610C2×C3×C4—68no—
611C2×C3×C4—62no—
612C2×C3×C4—62no—
613C2×C3×C4—62no—
614C2×C3×C4—62no—
615C2×C3×C4—62no—
616C2×C3×C4—124no—
617C2×C3×C4—124no—
618C2×C3×C4C23×D312yes—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D312yes—
621C2×C3×C4C23×D312yes—
622C2×C3×C4C23×D312yes—
623C2×C3×C4C23×D312yes—
624C2×C3×C4C24×C312yes—
625C2×C3×C4C24×C312yes—
626C2×C3×C4C24×C312yes—
627C2×C3×C4C24×C312yes—
628C2×C3×C4C24×C312yes—
629C2×C3×C4C24×C312yes—
630#67—28no—
631#67—44no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—44no—
638C2×Dic3C3×#4114yes—
639C2×Dic3C24×C312yes—
640C2×Dic3C24×C312yes—
641C2×Dic3C24×C312yes—
642C2×Dic3C24×C312yes—
643C2×Dic3C24×C312yes—
644C2×Dic3C24×C312yes—
645D12—44no—
646C4×D3—28no—
647C4×D3—44no—
648Dic6—28no—
649Dic6—44no—
650Dic6—44no—
651C2×C32—42no—
652C2×C32#54214yescomplemented
653C2×C32C22×#4111yescharacteristic
654C2×C32C2×H(5,𝔽2)11yescharacteristic
655C2×C32C2×2−1+411yescharacteristic
656C3×D3—42no—
657C3×D3—42no—
658C24—31no—
659C24—31no—
660C24C22×C3×D311yescharacteristic
661C2×Q8—34no—
662C2×Q8—34no—
663C2×Q8—34no—
664C2×Q8—64no—
665C2×Q8—122no—
666C2×Q8—122no—
667C2×D4—34no—
668C2×D4—34no—
669C2×D4—34no—
670C2×D4—64no—
671C2×D4—122no—
672C2×D4—122no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—34no—
680C22×C4—34no—
681C22×C4—34no—
682C22×C4—64no—
683C22×C4—122no—
684C22×C4—122no—
685C22×C4C22×C3×D311yescharacteristic
686C22×C4C22×C3×D311yescharacteristic
687C22×C4C22×C3×D311yescharacteristic
688C22×C4C22×C3×D311yescharacteristic
689C22×C4C22×C3×D311yescharacteristic
690C22×C4C22×C3×D311yescharacteristic
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4C22×C3×D314yes—
699C4⋊C4C22×C3×D314yes—
700C4⋊C4C22×C3×D314yes—
701C22⋊C4—34no—
702C22⋊C4—34no—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4C22×C3×D314yes—
711C22⋊C4C22×C3×D314yes—
712C22⋊C4C22×C3×D314yes—
713C42—34no—
714C42—34no—
715C42—34no—
716C42C22×C3×D314yes—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—44no—
731C22×C3—44no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—84no—
739C22×C3—124no—
740C22×C3—124no—
741C22×C3D3×#4112yes—
742C22×C3#100912yes—
743C22×C3#101012yes—
744C22×C3C2×C3×#4112yes—
745C22×C3C3×H(5,𝔽2)12yes—
746C22×C3C3×2−1+412yes—
747C22×C3C24×D311yescharacteristic
748C22×C3C25×C311yescharacteristic
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—44no—
756C2×D3—44no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—34no—
770C3×C4—42no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780C3×C4—62no—
781Dic3—22no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3C2×C3×#4114yes—
787C32C2×#54211yescharacteristic, complemented, Sylow
788C23—22no—
789C23—22no—
790C23—22no—
791C23—32no—
792C23—32no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23C23×C3×D312yes—
800C23C23×C3×D311yescharacteristic
801Q8—68no—
802Q8—124no—
803Q8—124no—
804D4—68no—
805D4—124no—
806D4—124no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—34no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—68no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—124no—
827C2×C4—124no—
828C2×C4C23×C3×D312yes—
829C2×C4C23×C3×D312yes—
830C2×C4C23×C3×D312yes—
831C2×C4C23×C3×D312yes—
832C2×C4C23×C3×D312yes—
833C2×C4C23×C3×D312yes—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3—42no—
840C2×C3—82no—
841C2×C3—122no—
842C2×C3—122no—
843C2×C3#571014yesdirect product factor
844C2×C3C3×#54214yescomplemented
845C2×C3C2×D3×#4111yescharacteristic
846C2×C3C2×#100911yescharacteristic
847C2×C3C2×#101011yescharacteristic
848C2×C3C22×C3×#4111yescharacteristic
849C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
850C2×C3C2×C3×2−1+411yescharacteristic
851D3—42no—
852D3—42no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—44no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—124no—
864C22—124no—
865C22C3×D3×#4112yes—
866C22C3×#100912yes—
867C22C3×#101012yes—
868C22C24×C3×D311yescharacteristic
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—34no—
876C4—62no—
877C4—62no—
878C4—62no—
879C4—62no—
880C4—62no—
881C3—21no—
882C3C2×#571011yescharacteristic, direct product factor
883C3C2×C3×#54211yescharacteristic, complemented
884C2—42no—
885C2—122no—
886C2—122no—
887C2C3×#571014yesdirect product factor
888C2C2×C3×D3×#4111yescharacteristic
889C2C2×C3×#100911yescharacteristic
890C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC2×C3×#884C2
hypercenterC2×C3×#126D3
hypocenterC3C2×C3×#542
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×#5710C2direct (N × H)
3. C2×C3×#898C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#896C2semidirect
6. C2×C3×#894C2semidirect
7. C2×C3×#892C2semidirect
8. C2×C3×#888C2semidirect
9. C2×C3×#886C2semidirect
10. C2×C3×#885C2semidirect
11. C2×C3×#885C2semidirect
13. C2×C3×#67⋊C4C2semidirect
14. C2×C3×#878C2semidirect
15. C2×C3×#875C2semidirect
16. C2×C3×C4×Dic6C2semidirect
18. C2×#5710C3direct (N × H)
28. C32×#126C22semidirect
55. C3×#898C22semidirect
56. C3×#897C22semidirect
57. C3×#896C22semidirect
58. C3×#894C22semidirect
59. C3×#892C22semidirect
60. C3×#888C22semidirect
61. C3×#886C22semidirect
62. C3×#885C22semidirect
63. C3×#885C22semidirect
65. C3×#67⋊C4C22semidirect
66. C3×#878C22semidirect
67. C3×#875C22semidirect
68. C3×C4×Dic6C22semidirect
73. C2×C3×#126D3semidirect
74. C2×C3×#126C2×C3semidirect
87. #5710C2×C3direct (N × H)
88. C2×#898C2×C3semidirect
89. C2×#897C2×C3semidirect
90. C2×#896C2×C3semidirect
91. C2×#894C2×C3semidirect
92. C2×#892C2×C3semidirect
93. C2×#888C2×C3semidirect
94. C2×#886C2×C3semidirect
95. C2×#885C2×C3semidirect
96. C2×#885C2×C3semidirect
98. C2×#67⋊C4C2×C3semidirect
99. C2×#878C2×C3semidirect
100. C2×#875C2×C3semidirect
101. C2×C4×Dic6C2×C3semidirect
183. C3×#126C2×D3semidirect
184. C3×#126C22×C3semidirect
256. #898C22×C3semidirect
257. #897C22×C3semidirect
258. #896C22×C3semidirect
259. #894C22×C3semidirect
260. #892C22×C3semidirect
261. #888C22×C3semidirect
262. #886C22×C3semidirect
263. #885C22×C3semidirect
264. #885C22×C3semidirect
266. #67⋊C4C22×C3semidirect
267. #878C22×C3semidirect
268. #875C22×C3semidirect
269. C4×Dic6C22×C3semidirect
319. C2×#126C3×D3semidirect
503. #126C2×C3×D3semidirect
652. C2×C32#542semidirect
787. C32C2×#542semidirect
843. C2×C3#5710direct (N × H)
844. C2×C3C3×#542semidirect
882. C3C2×#5710direct (N × H)
883. C3C2×C3×#542semidirect
887. C2C3×#5710direct (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×#57102
C2×C3×#8982
C2×C3×#8972
C2×C3×#8962
C2×C3×#8942
C2×C3×#8922
C2×C3×#8882
C2×C3×#8862
C2×C3×#8852
C2×C3×#8842
C2×C3×#67⋊C42
C2×C3×#8782
C2×C3×#8752
C2×C3×C4×Dic62
C2×C3×#5423
C2×#57103