Finite Group Databasebeta

← C2×C3×#5655 #11902488

Subgroups — C2×C3×#5655 #11902488

Order 1152.

3435 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C2×C32×#123C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×#5655C2116yesmaximal, direct product factor
7C2×C3×#896C211yesmaximal, characteristic, complemented
8C2×C3×#894C211yesmaximal, characteristic, complemented
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×#886C211yesmaximal, characteristic, complemented
12C2×C3×#884C211yesmaximal, characteristic, complemented
13C2×C3×#883C211yesmaximal, characteristic, complemented
14C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
15C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
16C2×C3×#878C211yesmaximal, characteristic, complemented
17C2×C3×#547—31nomaximal
18C2×#5655C311yesmaximal, characteristic, direct product factor
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic
27C23×C3×Dic3C2211yescharacteristic
28C2×C3×#237—28no—
29C2×C3×#237C2218yescomplemented
30C2×C3×#235—28no—
31C2×C3×#235C2218yescomplemented
32C22×C3×D12C2211yescharacteristic
33C22×C3×C4×D3C2211yescharacteristic
34C22×C3×C4×D3C2211yescharacteristic
35C22×C3×C4×D3C2211yescharacteristic
36C22×C3×C4×D3C2211yescharacteristic
37C22×C3×Dic6C2211yescharacteristic
38C22×C3×Dic6C2211yescharacteristic
39C32×#123C2218yescomplemented
40C2×C32×C4⋊C4C2211yescharacteristic
41C2×C32×C4⋊C4C2211yescharacteristic
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×C32×C22⋊C4C2211yescharacteristic
44C2×C32×C22⋊C4C2211yescharacteristic
45C2×C3×#217C2211yescharacteristic
46C3×#939C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×C4⋊Dic3C2211yescharacteristic
52C2×C3×C4⋊Dic3C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×Dic3⋊C4C2211yescharacteristic
56C2×C3×Dic3⋊C4C2211yescharacteristic
57C2×C3×Dic3⋊C4C2211yescharacteristic
58C2×C3×Dic3⋊C4C2211yescharacteristic
59C2×C3×Dic3⋊C4C2218yescomplemented
60C2×C3×C4×Dic3C2211yescharacteristic
61C3×#896C2218yescomplemented
62C3×#894C2218yescomplemented
63C3×D3×C4⋊C4C2218yescomplemented
64C3×#888C2218yescomplemented
65C3×#886C2218yescomplemented
66C3×#884C2218yescomplemented
67C3×#883C2218yescomplemented
68C3×#67⋊C4C2218yescomplemented
69C3×#67⋊C4C2218yescomplemented
70C3×#878C2218yescomplemented
71C22×C3×#41—31no—
72C22×C3×#41—31no—
73C22×#237C2×C311yescharacteristic, complemented
74C22×#235C2×C311yescharacteristic, complemented
75C3×#547—316no—
76C2×C3×C4⋊Q8—31no—
77C2×C3×#123—21no—
78C2×C3×#123—31no—
79C2×C3×#123—31no—
80C2×C3×#123—31no—
81C2×C3×#123D311yescharacteristic, complemented
82C2×C3×#123C2×C311yescharacteristic, complemented
83C2×C3×C22⋊Q8—31no—
84C2×C3×C22⋊Q8—31no—
85C2×C3×#121—31no—
86C2×C3×#121—31no—
87C2×C3×C4×D4—31no—
88C2×C3×C4×D4—31no—
89C22×C3×C4⋊C4—31no—
90C22×C3×C4⋊C4—31no—
91C2×#939C2×C311yescharacteristic, complemented
92C22×Dic3⋊C4C2×C311yescharacteristic, complemented
93#5655C2×C3116yesdirect product factor
94C2×#896C2×C311yescharacteristic, complemented
95C2×#894C2×C311yescharacteristic, complemented
96C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
97C2×#888C2×C311yescharacteristic, complemented
98C2×#886C2×C311yescharacteristic, complemented
99C2×#884C2×C311yescharacteristic, complemented
100C2×#883C2×C311yescharacteristic, complemented
101C2×#67⋊C4C2×C311yescharacteristic, complemented
102C2×#67⋊C4C2×C311yescharacteristic, complemented
103C2×#878C2×C311yescharacteristic, complemented
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C2×C32×D4—24no—
109C2×C32×D4C2314yes—
110C22×C32×C4—24no—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2314yes—
117C2×C3×#67—24no—
118C2×C3×#67—24no—
119C2×C3×#67—24no—
120C2×C3×#67D418yescomplemented
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3—24no—
126C22×C3×Dic3—24no—
127C22×C3×Dic3—24no—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2314yes—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C3×#237—232no—
138C3×#235—232no—
139C2×C3×D12—24no—
140C2×C3×D12C2314yes—
141C2×C3×C4×D3—24no—
142C2×C3×C4×D3—24no—
143C2×C3×C4×D3—24no—
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3C2314yes—
146C2×C3×C4×D3C2314yes—
147C2×C3×C4×D3C2314yes—
148C2×C3×C4×D3C2314yes—
149C2×C3×Dic6—24no—
150C2×C3×Dic6—24no—
151C2×C3×Dic6C2314yes—
152C2×C3×Dic6C2314yes—
153C32×C4⋊C4C2314yes—
154C32×C4⋊C4C2314yes—
155C32×C22⋊C4C2314yes—
156C32×C22⋊C4C2314yes—
157C32×C22⋊C4C2314yes—
158C3×#217C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×C4⋊Dic3C2314yes—
164C3×C4⋊Dic3C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×C4×Dic3C2314yes—
172C2×#547—31noSylow
173C2×C3×#41—38no—
174C2×C3×#41—38no—
175C2×C3×#41—68no—
176C2×C3×#41—68no—
177C22×C3×Q8—31no—
178C22×C3×Q8—31no—
179C22×C3×D4—21no—
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×D4C22×C311yescharacteristic
187C23×C3×C4—21no—
188C23×C3×C4—31no—
189C23×C3×C4—31no—
190C23×C3×C4—31no—
191C23×C3×C4—31no—
192C23×C3×C4—31no—
193C23×C3×C4—31no—
194C23×C3×C4—31no—
195C23×C3×C4C2×D311yescharacteristic
196C23×C3×C4C22×C311yescharacteristic
197C22×#67C22×C311yescharacteristic
198C22×#67C22×C311yescharacteristic
199C22×#67C22×C311yescharacteristic
200C22×#67C22×C311yescharacteristic
201C23×Dic3C22×C311yescharacteristic
202C23×Dic3C22×C311yescharacteristic
203C23×Dic3C22×C311yescharacteristic
204C2×#237—28no—
205C2×#237C22×C318yescomplemented
206C2×#235—28no—
207C2×#235C22×C318yescomplemented
208C22×D12C22×C311yescharacteristic
209C22×C4×D3C22×C311yescharacteristic
210C22×C4×D3C22×C311yescharacteristic
211C22×C4×D3C22×C311yescharacteristic
212C22×C4×D3C22×C311yescharacteristic
213C22×Dic6C22×C311yescharacteristic
214C22×Dic6C22×C311yescharacteristic
215C3×C4⋊Q8—38no—
216C3×#123—28no—
217C3×#123—38no—
218C3×#123—38no—
219C3×#123—38no—
220C3×#123C2×D318yescomplemented
221C3×#123C22×C318yescomplemented
222C3×C22⋊Q8—38no—
223C3×C22⋊Q8—38no—
224C3×#121—38no—
225C3×#121—38no—
226C3×C4×D4—38no—
227C3×C4×D4—38no—
228C2×C3×C4⋊C4—21no—
229C2×C3×C4⋊C4—21no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C4⋊C4—31no—
232C2×C3×C4⋊C4—31no—
233C2×C3×C4⋊C4—31no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C4⋊C4—31no—
236C2×C3×C4⋊C4—38no—
237C2×C3×C4⋊C4—31no—
238C2×C3×C4⋊C4—31no—
239C2×C3×C4⋊C4—38no—
240C2×C3×C4⋊C4C2×D311yescharacteristic
241C2×C3×C4⋊C4C2×D311yescharacteristic
242C2×C3×C4⋊C4C22×C311yescharacteristic
243C2×C3×C4⋊C4C22×C311yescharacteristic
244C2×C3×C22⋊C4—21no—
245C2×C3×C22⋊C4—21no—
246C2×C3×C22⋊C4—21no—
247C2×C3×C22⋊C4—31no—
248C2×C3×C22⋊C4—31no—
249C2×C3×C22⋊C4—31no—
250C2×C3×C22⋊C4—31no—
251C2×C3×C22⋊C4—31no—
252C2×C3×C22⋊C4C2×D311yescharacteristic
253C2×C3×C22⋊C4C2×D311yescharacteristic
254C2×C3×C22⋊C4C2×D311yescharacteristic
255C2×C3×C22⋊C4C22×C311yescharacteristic
256C2×C3×C22⋊C4C22×C311yescharacteristic
257C2×C3×C22⋊C4C22×C311yescharacteristic
258C2×C3×C42—31no—
259C2×#217C22×C311yescharacteristic
260#939C22×C318yescomplemented
261C2×(C2×D3)⋊C4C22×C311yescharacteristic
262C2×(C2×D3)⋊C4C22×C311yescharacteristic
263C2×(C2×D3)⋊C4C22×C311yescharacteristic
264C2×(C2×D3)⋊C4C22×C311yescharacteristic
265C2×C4⋊Dic3C22×C311yescharacteristic
266C2×C4⋊Dic3C22×C311yescharacteristic
267C2×Dic3⋊C4C22×C311yescharacteristic
268C2×Dic3⋊C4C22×C311yescharacteristic
269C2×Dic3⋊C4C22×C311yescharacteristic
270C2×Dic3⋊C4C22×C311yescharacteristic
271C2×Dic3⋊C4C22×C311yescharacteristic
272C2×Dic3⋊C4C22×C311yescharacteristic
273C2×Dic3⋊C4C22×C318yescomplemented
274C2×C4×Dic3C22×C311yescharacteristic
275#896C22×C318yescomplemented
276#894C22×C318yescomplemented
277D3×C4⋊C4C22×C318yescomplemented
278#888C22×C318yescomplemented
279#886C22×C318yescomplemented
280#884C22×C318yescomplemented
281#883C22×C318yescomplemented
282#67⋊C4C22×C318yescomplemented
283#67⋊C4C22×C318yescomplemented
284#878C22×C318yescomplemented
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32C2×D414yes—
291C23×C32C2412yes—
292C23×C32C2412yes—
293C23×C32C2411yescharacteristic
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2×D414yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C32×D4—28no—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4—22no—
306C2×C32×C4—28no—
307C2×C32×C4—22no—
308C2×C32×C4—22no—
309C2×C32×C4C2412yes—
310C2×C32×C4C2412yes—
311C2×C32×C4C2412yes—
312C2×C32×C4C2412yes—
313C2×C32×C4C2412yes—
314C3×#67—28no—
315C3×#67—28no—
316C3×#67—28no—
317C3×#67C2×D4116yescomplemented
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—28no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—28no—
324C2×C3×Dic3—28no—
325C2×C3×Dic3C2×D414yes—
326C2×C3×Dic3#4114yescomplemented
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C3×D12—28no—
334C3×C4×D3—28no—
335C3×C4×D3—28no—
336C3×C4×D3—28no—
337C3×C4×D3—28no—
338C3×Dic6—28no—
339C3×Dic6—28no—
340C22×#41—31no—
341C22×#41—31no—
342#547—316no—
343C2×C4⋊Q8—31no—
344C2×#123—31no—
345C2×#123—31no—
346C2×#123—31no—
347C2×#123C3×D311yescharacteristic, complemented
348C2×C22⋊Q8—31no—
349C2×C22⋊Q8—31no—
350C2×#121—31no—
351C2×#121—31no—
352C2×C4×D4—31no—
353C2×C4×D4—31no—
354C22×C4⋊C4—31no—
355C22×C4⋊C4—31no—
356C24×C3—21no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3C22×D311yescharacteristic
361C24×C3C22×D311yescharacteristic
362C24×C3C23×C311yescharacteristic
363C24×C3C23×C311yescharacteristic
364C23×D3C23×C311yescharacteristic
365C23×D3C23×C311yescharacteristic
366C3×#41—632no—
367C3×#41—632no—
368C2×C3×Q8—34no—
369C2×C3×Q8—34no—
370C2×C3×Q8—64no—
371C2×C3×Q8—64no—
372C2×C3×D4—24no—
373C2×C3×D4—24no—
374C2×C3×D4—24no—
375C2×C3×D4—38no—
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—44no—
382C2×C3×D4—64no—
383C2×C3×D4—64no—
384C2×C3×D4—64no—
385C2×C3×D4—64no—
386C2×C3×D4C22×D314yes—
387C2×C3×D4C23×C314yes—
388C22×C3×C4—24no—
389C22×C3×C4—24no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—24no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—34no—
399C22×C3×C4—34no—
400C22×C3×C4—34no—
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—34no—
409C22×C3×C4—44no—
410C22×C3×C4—64no—
411C22×C3×C4—64no—
412C22×C3×C4—64no—
413C22×C3×C4—64no—
414C22×C3×C4—64no—
415C22×C3×C4—64no—
416C22×C3×C4—64no—
417C22×C3×C4C22×D314yes—
418C22×C3×C4C22×D311yescharacteristic
419C22×C3×C4C22×D311yescharacteristic
420C22×C3×C4C22×D311yescharacteristic
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C23×C311yescharacteristic
424C22×C3×C4C23×C311yescharacteristic
425C22×C3×C4C23×C311yescharacteristic
426C22×C3×C4C23×C311yescharacteristic
427C22×C3×C4C23×C311yescharacteristic
428C22×C3×C4C23×C314yes—
429C2×#67—24no—
430C2×#67—24no—
431C2×#67—24no—
432C2×#67C3×D418yescomplemented
433C2×#67C23×C314yes—
434C2×#67C23×C314yes—
435C2×#67C23×C314yes—
436C2×#67C23×C314yes—
437C22×Dic3—24no—
438C22×Dic3—24no—
439C22×Dic3—24no—
440C22×Dic3C23×C314yes—
441C22×Dic3C23×C314yes—
442C22×Dic3C23×C314yes—
443C22×Dic3C23×C311yescharacteristic
444C22×Dic3C23×C311yescharacteristic
445C22×Dic3C23×C311yescharacteristic
446C22×Dic3C23×C311yescharacteristic
447C22×Dic3C23×C311yescharacteristic
448C22×Dic3C23×C311yescharacteristic
449#237—232no—
450#235—232no—
451C2×D12—24no—
452C2×D12C23×C314yes—
453C2×C4×D3—24no—
454C2×C4×D3—24no—
455C2×C4×D3—24no—
456C2×C4×D3—24no—
457C2×C4×D3C23×C314yes—
458C2×C4×D3C23×C314yes—
459C2×C4×D3C23×C314yes—
460C2×C4×D3C23×C314yes—
461C2×Dic6—24no—
462C2×Dic6—24no—
463C2×Dic6C23×C314yes—
464C2×Dic6C23×C314yes—
465C3×C4⋊C4—24no—
466C3×C4⋊C4—24no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—34no—
469C3×C4⋊C4—34no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C4⋊C4—34no—
475C3×C4⋊C4C22×D314yes—
476C3×C4⋊C4C22×D314yes—
477C3×C4⋊C4C23×C314yes—
478C3×C4⋊C4C23×C314yes—
479C3×C22⋊C4—24no—
480C3×C22⋊C4—24no—
481C3×C22⋊C4—24no—
482C3×C22⋊C4—34no—
483C3×C22⋊C4—34no—
484C3×C22⋊C4—34no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4—34no—
487C3×C22⋊C4C22×D314yes—
488C3×C22⋊C4C22×D314yes—
489C3×C22⋊C4C22×D314yes—
490C3×C22⋊C4C23×C314yes—
491C3×C22⋊C4C23×C314yes—
492C3×C22⋊C4C23×C314yes—
493C3×C42—34no—
494#217C23×C314yes—
495(C2×D3)⋊C4C23×C314yes—
496(C2×D3)⋊C4C23×C314yes—
497(C2×D3)⋊C4C23×C314yes—
498(C2×D3)⋊C4C23×C314yes—
499C4⋊Dic3C23×C314yes—
500C4⋊Dic3C23×C314yes—
501Dic3⋊C4C23×C314yes—
502Dic3⋊C4C23×C314yes—
503Dic3⋊C4C23×C314yes—
504Dic3⋊C4C23×C314yes—
505Dic3⋊C4C23×C314yes—
506Dic3⋊C4C23×C314yes—
507C4×Dic3C23×C314yes—
508C22×C32—28no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—44no—
515C22×C32C22×D414yes—
516C22×C32C22×D412yes—
517C22×C32C2×#4112yes—
518C22×C322−1+412yes—
519C22×C32C2511yescharacteristic
520C2×C3×D3—28no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—44no—
527C2×C3×D3C22×D414yes—
528C32×C4—22no—
529C32×C4—22no—
530C32×C4—22no—
531C32×C4—22no—
532C32×C4—22no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3C22×D414yes—
538C3×Dic3C2×#4114yescomplemented
539C2×#41—38no—
540C2×#41—38no—
541C2×#41—68no—
542C2×#41—68no—
543C22×Q8—31no—
544C22×Q8—31no—
545C22×D4—31no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4C2×C3×D311yescharacteristic
551C23×C4—31no—
552C23×C4—31no—
553C23×C4—31no—
554C23×C4—31no—
555C23×C4—31no—
556C23×C4—31no—
557C23×C4—31no—
558C23×C4C2×C3×D311yescharacteristic
559C4⋊Q8—38no—
560#123—38no—
561#123—38no—
562#123—38no—
563#123C2×C3×D318yescomplemented
564C22⋊Q8—38no—
565C22⋊Q8—38no—
566#121—38no—
567#121—38no—
568C4×D4—38no—
569C4×D4—38no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—31no—
574C2×C4⋊C4—31no—
575C2×C4⋊C4—31no—
576C2×C4⋊C4—38no—
577C2×C4⋊C4—31no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—38no—
580C2×C4⋊C4C2×C3×D311yescharacteristic
581C2×C4⋊C4C2×C3×D311yescharacteristic
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4C2×C3×D311yescharacteristic
588C2×C22⋊C4C2×C3×D311yescharacteristic
589C2×C22⋊C4C2×C3×D311yescharacteristic
590C2×C42—31no—
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—22no—
600C23×C3—22no—
601C23×C3—21no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—24no—
605C23×C3—34no—
606C23×C3—32no—
607C23×C3—32no—
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×C3D3×D414yes—
619C23×C3C2×C3×D414yes—
620C23×C3C23×D312yes—
621C23×C3C23×D312yes—
622C23×C3C23×D311yescharacteristic
623C23×C3C24×C312yes—
624C23×C3C24×C312yes—
625C23×C3C24×C311yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3C2×C3×D414yes—
632C22×D3C24×C312yes—
633C22×D3C24×C312yes—
634C3×Q8—68no—
635C3×Q8—68no—
636C3×D4—28no—
637C3×D4—28no—
638C3×D4—316no—
639C3×D4—48no—
640C3×D4—68no—
641C3×D4—68no—
642C3×D4—68no—
643C3×D4—68no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—28no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—28no—
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—34no—
662C2×C3×C4—34no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—42no—
670C2×C3×C4—42no—
671C2×C3×C4—42no—
672C2×C3×C4—42no—
673C2×C3×C4—48no—
674C2×C3×C4—42no—
675C2×C3×C4—68no—
676C2×C3×C4—68no—
677C2×C3×C4—68no—
678C2×C3×C4—68no—
679C2×C3×C4—68no—
680C2×C3×C4—68no—
681C2×C3×C4—62no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—68no—
685C2×C3×C4—62no—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D312yes—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C24×C312yes—
692C2×C3×C4C24×C312yes—
693C2×C3×C4C24×C312yes—
694C2×C3×C4C24×C312yes—
695C2×C3×C4C24×C312yes—
696#67—28no—
697#67—28no—
698#67—28no—
699#67C2×C3×D4116yescomplemented
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—28no—
704C2×Dic3—22no—
705C2×Dic3—28no—
706C2×Dic3—28no—
707C2×Dic3C2×C3×D414yes—
708C2×Dic3C3×#4114yescomplemented
709C2×Dic3C24×C312yes—
710C2×Dic3C24×C312yes—
711C2×Dic3C24×C312yes—
712C2×Dic3C24×C312yes—
713C2×Dic3C24×C312yes—
714C2×Dic3C24×C312yes—
715D12—28no—
716C4×D3—28no—
717C4×D3—28no—
718C4×D3—28no—
719C4×D3—28no—
720Dic6—28no—
721Dic6—28no—
722C2×C32—24no—
723C2×C32—42no—
724C2×C32#54714yescomplemented
725C2×C32C23×D411yescharacteristic
726C2×C32C22×#4111yescharacteristic
727C2×C32C2×2−1+411yescharacteristic
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24C22×C3×D311yescharacteristic
733C24C22×C3×D311yescharacteristic
734#41—632no—
735#41—632no—
736C2×Q8—34no—
737C2×Q8—34no—
738C2×Q8—64no—
739C2×Q8—64no—
740C2×D4—24no—
741C2×D4—34no—
742C2×D4—38no—
743C2×D4—34no—
744C2×D4—34no—
745C2×D4—34no—
746C2×D4—34no—
747C2×D4—64no—
748C2×D4—64no—
749C2×D4—64no—
750C2×D4—64no—
751C2×D4C22×C3×D314yes—
752C22×C4—24no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—34no—
760C22×C4—34no—
761C22×C4—34no—
762C22×C4—34no—
763C22×C4—34no—
764C22×C4—34no—
765C22×C4—34no—
766C22×C4—64no—
767C22×C4—64no—
768C22×C4—64no—
769C22×C4—64no—
770C22×C4—64no—
771C22×C4—64no—
772C22×C4—64no—
773C22×C4C22×C3×D311yescharacteristic
774C22×C4C22×C3×D311yescharacteristic
775C22×C4C22×C3×D311yescharacteristic
776C22×C4C22×C3×D311yescharacteristic
777C22×C4C22×C3×D311yescharacteristic
778C22×C4C22×C3×D314yes—
779C4⋊C4—34no—
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—34no—
784C4⋊C4—34no—
785C4⋊C4—34no—
786C4⋊C4—34no—
787C4⋊C4C22×C3×D314yes—
788C4⋊C4C22×C3×D314yes—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—34no—
792C22⋊C4—34no—
793C22⋊C4—34no—
794C22⋊C4C22×C3×D314yes—
795C22⋊C4C22×C3×D314yes—
796C22⋊C4C22×C3×D314yes—
797C42—34no—
798C22×C3—28no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—28no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—24no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—21no—
815C22×C3—34no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—48no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—44no—
823C22×C3—44no—
824C22×C3—68no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—84no—
831C22×C3—124no—
832C22×C3C2×D3×D414yes—
833C22×C3C2×D3×D412yes—
834C22×C3D3×#4112yes—
835C22×C3#101012yes—
836C22×C3C22×C3×D414yes—
837C22×C3C22×C3×D412yes—
838C22×C3C2×C3×#4112yes—
839C22×C3C3×2−1+412yes—
840C22×C3C24×D311yescharacteristic
841C22×C3C25×C311yescharacteristic
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—28no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—44no—
849C2×D3C22×C3×D414yes—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—34no—
861C3×C4—34no—
862C3×C4—42no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871Dic3—22no—
872Dic3—22no—
873Dic3—22no—
874Dic3—22no—
875Dic3C22×C3×D414yes—
876Dic3C2×C3×#4114yescomplemented
877C32C2×#54711yescharacteristic, complemented, Sylow
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—34no—
884C23—32no—
885C23—32no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23C3×D3×D414yes—
892C23C23×C3×D312yes—
893C23C23×C3×D312yes—
894C23C23×C3×D311yescharacteristic
895Q8—68no—
896Q8—68no—
897D4—28no—
898D4—316no—
899D4—68no—
900D4—68no—
901D4—68no—
902D4—68no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—28no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—34no—
910C2×C4—34no—
911C2×C4—32no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—68no—
918C2×C4—68no—
919C2×C4—68no—
920C2×C4—68no—
921C2×C4—68no—
922C2×C4—68no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—68no—
927C2×C4—62no—
928C2×C4C23×C3×D312yes—
929C2×C4C23×C3×D312yes—
930C2×C4C23×C3×D312yes—
931C2×C4C23×C3×D312yes—
932C2×C4C23×C3×D312yes—
933C2×C3—24no—
934C2×C3—24no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—24no—
939C2×C3—44no—
940C2×C3—42no—
941C2×C3—42no—
942C2×C3—64no—
943C2×C3—82no—
944C2×C3—122no—
945C2×C3#565514yesdirect product factor
946C2×C3C3×#54714yescomplemented
947C2×C3C22×D3×D411yescharacteristic
948C2×C3C2×D3×#4111yescharacteristic
949C2×C3C2×#101011yescharacteristic
950C2×C3C23×C3×D411yescharacteristic
951C2×C3C22×C3×#4111yescharacteristic
952C2×C3C2×C3×2−1+411yescharacteristic
953D3—24no—
954D3—42no—
955C22—22no—
956C22—22no—
957C22—28no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—34no—
962C22—44no—
963C22—62no—
964C22—62no—
965C22—68no—
966C22—62no—
967C22—62no—
968C22—62no—
969C22—124no—
970C22C2×C3×D3×D414yes—
971C22C2×C3×D3×D412yes—
972C22C3×D3×#4112yes—
973C22C3×#101012yes—
974C22C24×C3×D311yescharacteristic
975C4—22no—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—34no—
981C4—34no—
982C4—62no—
983C4—62no—
984C4—62no—
985C4—62no—
986C3—21no—
987C3C2×#565511yescharacteristic, direct product factor
988C3C2×C3×#54711yescharacteristic, complemented
989C2—24no—
990C2—42no—
991C2—64no—
992C2—122no—
993C2C3×#565514yesdirect product factor
994C2C22×C3×D3×D411yescharacteristic
995C2C2×C3×D3×#4111yescharacteristic
996C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#123C2
socleC23×C32C24
hypercenterC2×C3×#123D3
hypocenterC3C2×C3×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×C3×#235C2semidirect
3. C2×C32×#123C2semidirect
4. C2×C3×#939C2semidirect
5. C22×C3×Dic3⋊C4C2semidirect
6. C3×#5655C2direct (N × H)
7. C2×C3×#896C2semidirect
8. C2×C3×#894C2semidirect
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#888C2semidirect
11. C2×C3×#886C2semidirect
12. C2×C3×#884C2semidirect
13. C2×C3×#883C2semidirect
14. C2×C3×#67⋊C4C2semidirect
15. C2×C3×#67⋊C4C2semidirect
16. C2×C3×#878C2semidirect
18. C2×#5655C3direct (N × H)
29. C2×C3×#237C22semidirect
31. C2×C3×#235C22semidirect
39. C32×#123C22semidirect
46. C3×#939C22semidirect
59. C2×C3×Dic3⋊C4C22semidirect
61. C3×#896C22semidirect
62. C3×#894C22semidirect
63. C3×D3×C4⋊C4C22semidirect
64. C3×#888C22semidirect
65. C3×#886C22semidirect
66. C3×#884C22semidirect
67. C3×#883C22semidirect
68. C3×#67⋊C4C22semidirect
69. C3×#67⋊C4C22semidirect
70. C3×#878C22semidirect
73. C22×#237C2×C3semidirect
74. C22×#235C2×C3semidirect
81. C2×C3×#123D3semidirect
82. C2×C3×#123C2×C3semidirect
91. C2×#939C2×C3semidirect
92. C22×Dic3⋊C4C2×C3semidirect
93. #5655C2×C3direct (N × H)
94. C2×#896C2×C3semidirect
95. C2×#894C2×C3semidirect
96. C2×D3×C4⋊C4C2×C3semidirect
97. C2×#888C2×C3semidirect
98. C2×#886C2×C3semidirect
99. C2×#884C2×C3semidirect
100. C2×#883C2×C3semidirect
101. C2×#67⋊C4C2×C3semidirect
102. C2×#67⋊C4C2×C3semidirect
103. C2×#878C2×C3semidirect
120. C2×C3×#67D4semidirect
205. C2×#237C22×C3semidirect
207. C2×#235C22×C3semidirect
220. C3×#123C2×D3semidirect
221. C3×#123C22×C3semidirect
260. #939C22×C3semidirect
273. C2×Dic3⋊C4C22×C3semidirect
275. #896C22×C3semidirect
276. #894C22×C3semidirect
277. D3×C4⋊C4C22×C3semidirect
278. #888C22×C3semidirect
279. #886C22×C3semidirect
280. #884C22×C3semidirect
281. #883C22×C3semidirect
282. #67⋊C4C22×C3semidirect
283. #67⋊C4C22×C3semidirect
284. #878C22×C3semidirect
317. C3×#67C2×D4semidirect
326. C2×C3×Dic3#41semidirect
347. C2×#123C3×D3semidirect
432. C2×#67C3×D4semidirect
538. C3×Dic3C2×#41semidirect
563. #123C2×C3×D3semidirect
699. #67C2×C3×D4semidirect
708. C2×Dic3C3×#41semidirect
724. C2×C32#547semidirect
876. Dic3C2×C3×#41semidirect
877. C32C2×#547semidirect
945. C2×C3#5655direct (N × H)
946. C2×C3C3×#547semidirect
987. C3C2×#5655direct (N × H)
988. C3C2×C3×#547semidirect
993. C2C3×#5655direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C3×#2352
C2×C32×#1232
C2×C3×#9392
C22×C3×Dic3⋊C42
C3×#56552
C2×C3×#8962
C2×C3×#8942
C2×C3×D3×C4⋊C42
C2×C3×#8882
C2×C3×#8862
C2×C3×#8842
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×#8782
C2×C3×#5473
C2×#56553