Finite Group Databasebeta

← C2×C3×#5538 #11900581

Subgroups — C2×C3×#5538 #11900581

Order 1152.

2677 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C2×C3×#926C211yesmaximal, characteristic, complemented
7C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
8C3×#5538C2116yesmaximal, direct product factor
9C2×C3×#898C211yesmaximal, characteristic, complemented
10C2×C3×#889C211yesmaximal, characteristic, complemented
11C2×C3×#886C211yesmaximal, characteristic, complemented
12C2×C3×#885C211yesmaximal, characteristic, complemented
13C2×C3×#879C211yesmaximal, characteristic, complemented
14C2×C3×#878C211yesmaximal, characteristic, complemented
15C2×C3×#872C211yesmaximal, characteristic, complemented
16C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
17C2×C3×#529—31nomaximal
18C2×#5538C311yesmaximal, characteristic, direct product factor
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C32×C4×D4C2218yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C42C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×#939C2218yes—
38C3×#935C2218yescomplemented
39C3×C4×#67C2218yescomplemented
40C3×C4×#67C2218yescomplemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C3×#926C2218yescomplemented
46C2×C3×C4⋊Dic3C2211yescharacteristic
47C2×C3×C4⋊Dic3C2211yescharacteristic
48C2×C3×C4⋊Dic3C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C2×C3×Dic3⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×C4×Dic3C2211yescharacteristic
56C2×C3×C4×Dic3C2211yescharacteristic
57C2×C3×C4×Dic3C2211yescharacteristic
58C2×C3×C4×Dic3C2211yescharacteristic
59C2×C3×C4×Dic3C2211yescharacteristic
60C2×C3×C4×Dic3C2218yescomplemented
61C3×#898C2218yescomplemented
62C3×#889C2218yescomplemented
63C3×#886C2218yescomplemented
64C3×#885C2218yescomplemented
65C3×#879C2218yescomplemented
66C3×#878C2218yescomplemented
67C3×#872C2218yescomplemented
68C3×C4×Dic6C2218yescomplemented
69C3×#529—316no—
70C2×C3×#126—31no—
71C2×C3×#126—31no—
72C2×C3×#125—31no—
73C2×C3×#124—31no—
74C2×C3×#123—31no—
75C2×C3×#123—31no—
76C2×C3×C22⋊Q8—31no—
77C2×C3×#121—31no—
78C2×C3×C4×Q8—31no—
79C2×C3×C4×D4—21no—
80C2×C3×C4×D4—31no—
81C2×C3×C4×D4—31no—
82C2×C3×C4×D4D311yescharacteristic, complemented
83C2×C3×C4×D4C2×C311yescharacteristic, complemented
84C2×C3×#117—31no—
85C2×C3×#117—31no—
86C22×C3×C42—31no—
87C2×#939C2×C311yescharacteristic
88C2×#935C2×C311yescharacteristic, complemented
89C2×C4×#67C2×C311yescharacteristic, complemented
90C2×C4×#67C2×C311yescharacteristic, complemented
91C2×#926C2×C311yescharacteristic, complemented
92C22×C4×Dic3C2×C311yescharacteristic, complemented
93#5538C2×C3116yesdirect product factor
94C2×#898C2×C311yescharacteristic, complemented
95C2×#889C2×C311yescharacteristic, complemented
96C2×#886C2×C311yescharacteristic, complemented
97C2×#885C2×C311yescharacteristic, complemented
98C2×#879C2×C311yescharacteristic, complemented
99C2×#878C2×C311yescharacteristic, complemented
100C2×#872C2×C311yescharacteristic, complemented
101C2×C4×Dic6C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C2×C32×D4—24no—
106C2×C32×D4C2314yes—
107C22×C32×C4—24no—
108C22×C32×C4—24no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2314yes—
115C22×C32×C4C2311yescharacteristic
116C2×C3×#67—24no—
117C2×C3×#67—24no—
118C2×C3×#67C2314yes—
119C2×C3×#67C2314yes—
120C22×C3×Dic3—24no—
121C22×C3×Dic3—24no—
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6C2314yes—
135C32×C4⋊C4C2314yes—
136C32×C22⋊C4C2314yes—
137C32×C22⋊C4C2314yes—
138C32×C42C2314yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×C4⋊Dic3C2314yes—
149C3×C4⋊Dic3C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×C4×Dic3C2314yes—
157C3×C4×Dic3C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161C2×#529—31noSylow
162C22×C3×Q8—31no—
163C22×C3×D4—21no—
164C22×C3×D4—31no—
165C22×C3×D4—31no—
166C22×C3×D4C2×D311yescharacteristic
167C22×C3×D4C22×C311yescharacteristic
168C23×C3×C4—21no—
169C23×C3×C4—21no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C23×C3×C4—31no—
173C23×C3×C4C2×D311yescharacteristic
174C23×C3×C4C2×D311yescharacteristic
175C23×C3×C4C22×C311yescharacteristic
176C23×C3×C4C22×C311yescharacteristic
177C22×#67C22×C311yescharacteristic
178C22×#67C22×C311yescharacteristic
179C23×Dic3C22×C311yescharacteristic
180C23×Dic3C22×C311yescharacteristic
181C22×C4×D3C22×C311yescharacteristic
182C22×Dic6C22×C311yescharacteristic
183C3×#126—38no—
184C3×#126—38no—
185C3×#125—38no—
186C3×#124—38no—
187C3×#123—38no—
188C3×#123—38no—
189C3×C22⋊Q8—38no—
190C3×#121—38no—
191C3×C4×Q8—38no—
192C3×C4×D4—28no—
193C3×C4×D4—38no—
194C3×C4×D4—38no—
195C3×C4×D4C2×D318yescomplemented
196C3×C4×D4C22×C318yescomplemented
197C3×#117—38no—
198C3×#117—38no—
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⋊C4—31no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4C2×D311yescharacteristic
210C2×C3×C4⋊C4C22×C311yescharacteristic
211C2×C3×C22⋊C4—21no—
212C2×C3×C22⋊C4—21no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
222C2×C3×C22⋊C4C2×D311yescharacteristic
223C2×C3×C22⋊C4C22×C311yescharacteristic
224C2×C3×C22⋊C4C22×C311yescharacteristic
225C2×C3×C42—21no—
226C2×C3×C42—31no—
227C2×C3×C42—31no—
228C2×C3×C42—38no—
229C2×C3×C42—31no—
230C2×C3×C42—31no—
231C2×C3×C42—31no—
232C2×C3×C42C2×D311yescharacteristic
233C2×C3×C42C22×C311yescharacteristic
234C2×#217C22×C311yescharacteristic
235C2×#217C22×C311yescharacteristic
236C2×#217C22×C311yescharacteristic
237C2×#217C22×C311yescharacteristic
238#939C22×C318yes—
239#935C22×C318yescomplemented
240C4×#67C22×C318yescomplemented
241C4×#67C22×C318yescomplemented
242C2×(C2×D3)⋊C4C22×C311yescharacteristic
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×(C2×D3)⋊C4C22×C311yescharacteristic
245C2×(C2×D3)⋊C4C22×C311yescharacteristic
246#926C22×C318yescomplemented
247C2×C4⋊Dic3C22×C311yescharacteristic
248C2×C4⋊Dic3C22×C311yescharacteristic
249C2×C4⋊Dic3C22×C311yescharacteristic
250C2×Dic3⋊C4C22×C311yescharacteristic
251C2×Dic3⋊C4C22×C311yescharacteristic
252C2×Dic3⋊C4C22×C311yescharacteristic
253C2×Dic3⋊C4C22×C311yescharacteristic
254C2×Dic3⋊C4C22×C311yescharacteristic
255C2×Dic3⋊C4C22×C311yescharacteristic
256C2×C4×Dic3C22×C311yescharacteristic
257C2×C4×Dic3C22×C311yescharacteristic
258C2×C4×Dic3C22×C311yescharacteristic
259C2×C4×Dic3C22×C311yescharacteristic
260C2×C4×Dic3C22×C311yescharacteristic
261C2×C4×Dic3C22×C318yescomplemented
262#898C22×C318yescomplemented
263#889C22×C318yescomplemented
264#886C22×C318yescomplemented
265#885C22×C318yescomplemented
266#879C22×C318yescomplemented
267#878C22×C318yescomplemented
268#872C22×C318yescomplemented
269C4×Dic6C22×C318yescomplemented
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C32×D4—28no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4—22no—
287C2×C32×C4—22no—
288C2×C32×C4—28no—
289C2×C32×C4—28no—
290C2×C32×C4#4114yes—
291C2×C32×C4C2412yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C3×#67—28no—
297C3×#67—28no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—28no—
306C2×C3×Dic3#4114yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C3×C4×D3—28no—
315C3×Dic6—28no—
316#529—316no—
317C2×#126—31no—
318C2×#126—31no—
319C2×#125—31no—
320C2×#124—31no—
321C2×#123—31no—
322C2×#123—31no—
323C2×C22⋊Q8—31no—
324C2×#121—31no—
325C2×C4×Q8—31no—
326C2×C4×D4—31no—
327C2×C4×D4—31no—
328C2×C4×D4C3×D311yescharacteristic, complemented
329C2×#117—31no—
330C2×#117—31no—
331C22×C42—31no—
332C24×C3—21no—
333C24×C3—21no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C24×C3C23×C311yescharacteristic
338C24×C3C23×C311yescharacteristic
339C23×D3C23×C311yescharacteristic
340C2×C3×Q8—34no—
341C2×C3×Q8—64no—
342C2×C3×D4—28no—
343C2×C3×D4—24no—
344C2×C3×D4—24no—
345C2×C3×D4—24no—
346C2×C3×D4—34no—
347C2×C3×D4—34no—
348C2×C3×D4—64no—
349C2×C3×D4—64no—
350C2×C3×D4C22×D314yes—
351C2×C3×D4C23×C314yes—
352C22×C3×C4—24no—
353C22×C3×C4—24no—
354C22×C3×C4—24no—
355C22×C3×C4—24no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—24no—
362C22×C3×C4—24no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—34no—
368C22×C3×C4—34no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—34no—
373C22×C3×C4—44no—
374C22×C3×C4—44no—
375C22×C3×C4—64no—
376C22×C3×C4—64no—
377C22×C3×C4—64no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D314yes—
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D314yes—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C314yes—
387C22×C3×C4C23×C311yescharacteristic
388C22×C3×C4C23×C311yescharacteristic
389C22×C3×C4C23×C311yescharacteristic
390C22×C3×C4C23×C314yes—
391C22×C3×C4C23×C311yescharacteristic
392C2×#67—24no—
393C2×#67—24no—
394C2×#67C23×C314yes—
395C2×#67C23×C314yes—
396C22×Dic3—24no—
397C22×Dic3—24no—
398C22×Dic3C23×C314yes—
399C22×Dic3C23×C314yes—
400C22×Dic3C23×C311yescharacteristic
401C22×Dic3C23×C311yescharacteristic
402C22×Dic3C23×C311yescharacteristic
403C22×Dic3C23×C311yescharacteristic
404C22×Dic3C23×C311yescharacteristic
405C22×Dic3C23×C311yescharacteristic
406C22×Dic3C23×C311yescharacteristic
407C2×C4×D3—24no—
408C2×C4×D3C23×C314yes—
409C2×Dic6—24no—
410C2×Dic6C23×C314yes—
411C3×C4⋊C4—24no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4C22×D314yes—
422C3×C4⋊C4C23×C314yes—
423C3×C22⋊C4—24no—
424C3×C22⋊C4—24no—
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⋊C4C23×C314yes—
436C3×C22⋊C4C23×C314yes—
437C3×C42—24no—
438C3×C42—34no—
439C3×C42—34no—
440C3×C42—34no—
441C3×C42—34no—
442C3×C42—34no—
443C3×C42C22×D314yes—
444C3×C42C23×C314yes—
445#217C23×C314yes—
446#217C23×C314yes—
447#217C23×C314yes—
448#217C23×C314yes—
449(C2×D3)⋊C4C23×C314yes—
450(C2×D3)⋊C4C23×C314yes—
451(C2×D3)⋊C4C23×C314yes—
452(C2×D3)⋊C4C23×C314yes—
453C4⋊Dic3C23×C314yes—
454C4⋊Dic3C23×C314yes—
455C4⋊Dic3C23×C314yes—
456Dic3⋊C4C23×C314yes—
457Dic3⋊C4C23×C314yes—
458Dic3⋊C4C23×C314yes—
459Dic3⋊C4C23×C314yes—
460Dic3⋊C4C23×C314yes—
461Dic3⋊C4C23×C314yes—
462C4×Dic3C23×C314yes—
463C4×Dic3C23×C314yes—
464C4×Dic3C23×C314yes—
465C4×Dic3C23×C314yes—
466C4×Dic3C23×C314yes—
467C22×C32—22no—
468C22×C32—28no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—44no—
474C22×C32C2×#4114yes—
475C22×C32C2×#4112yes—
476C22×C32C2×#4112yes—
477C22×C32C2×#4112yes—
478C22×C32C2511yescharacteristic
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—44no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—22no—
487C32×C4C2×#4114yes—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3C2×#4114yes—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4C2×C3×D311yescharacteristic
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—31no—
502C23×C4C2×C3×D311yescharacteristic
503C23×C4C2×C3×D311yescharacteristic
504#126—38no—
505#126—38no—
506#125—38no—
507#124—38no—
508#123—38no—
509#123—38no—
510C22⋊Q8—38no—
511#121—38no—
512C4×Q8—38no—
513C4×D4—38no—
514C4×D4—38no—
515C4×D4C2×C3×D318yescomplemented
516#117—38no—
517#117—38no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—31no—
526C2×C4⋊C4—31no—
527C2×C4⋊C4C2×C3×D311yescharacteristic
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⋊C4—31no—
536C2×C22⋊C4C2×C3×D311yescharacteristic
537C2×C22⋊C4C2×C3×D311yescharacteristic
538C2×C42—31no—
539C2×C42—31no—
540C2×C42—31no—
541C2×C42—31no—
542C2×C42—31no—
543C2×C42—38no—
544C2×C42C2×C3×D311yescharacteristic
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—24no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—21no—
557C23×C3—22no—
558C23×C3—22no—
559C23×C3—24no—
560C23×C3—32no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3#23514yes—
569C23×C3C3×#4114yes—
570C23×C3C23×D312yes—
571C23×C3C23×D312yes—
572C23×C3C23×D311yescharacteristic
573C23×C3C24×C312yes—
574C23×C3C24×C312yes—
575C23×C3C24×C311yescharacteristic
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3C24×C312yes—
580C3×Q8—68no—
581C3×D4—216no—
582C3×D4—28no—
583C3×D4—28no—
584C3×D4—68no—
585C3×D4—68no—
586C2×C3×C4—24no—
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—28no—
596C2×C3×C4—28no—
597C2×C3×C4—28no—
598C2×C3×C4—28no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—24no—
605C2×C3×C4—34no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—48no—
614C2×C3×C4—48no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—42no—
618C2×C3×C4—68no—
619C2×C3×C4—68no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—68no—
627C2×C3×C4#23714yes—
628C2×C3×C4C3×#4114yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C24×C312yes—
635C2×C3×C4C24×C312yes—
636C2×C3×C4C24×C312yes—
637C2×C3×C4C24×C312yes—
638C2×C3×C4C24×C312yes—
639#67—28no—
640#67—28no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—28no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—28no—
649C2×Dic3C3×#4114yes—
650C2×Dic3C24×C312yes—
651C2×Dic3C24×C312yes—
652C2×Dic3C24×C312yes—
653C2×Dic3C24×C312yes—
654C2×Dic3C24×C312yes—
655C2×Dic3C24×C312yes—
656C2×Dic3C24×C312yes—
657C4×D3—28no—
658Dic6—28no—
659C2×C32—24no—
660C2×C32—42no—
661C2×C32#52914yescomplemented
662C2×C32C22×#4111yescharacteristic
663C2×C32C22×#4111yescharacteristic
664C2×C32C22×#4111yescharacteristic
665C3×D3—42no—
666C24—31no—
667C24C22×C3×D311yescharacteristic
668C24C22×C3×D311yescharacteristic
669C2×Q8—34no—
670C2×Q8—64no—
671C2×D4—24no—
672C2×D4—34no—
673C2×D4—34no—
674C2×D4—64no—
675C2×D4—64no—
676C2×D4C22×C3×D314yes—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—34no—
684C22×C4—34no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—34no—
689C22×C4—64no—
690C22×C4—64no—
691C22×C4—64no—
692C22×C4C22×C3×D311yescharacteristic
693C22×C4C22×C3×D314yes—
694C22×C4C22×C3×D311yescharacteristic
695C22×C4C22×C3×D311yescharacteristic
696C22×C4C22×C3×D311yescharacteristic
697C22×C4C22×C3×D314yes—
698C22×C4C22×C3×D311yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—34no—
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4—34no—
707C4⋊C4—34no—
708C4⋊C4C22×C3×D314yes—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—34no—
717C22⋊C4C22×C3×D314yes—
718C22⋊C4C22×C3×D314yes—
719C42—34no—
720C42—34no—
721C42—34no—
722C42—34no—
723C42—34no—
724C42C22×C3×D314yes—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—28no—
730C22×C3—28no—
731C22×C3—24no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—24no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—48no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—48no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—124no—
755C22×C3C2×#23514yes—
756C22×C3C2×#23512yes—
757C22×C3C2×#23712yes—
758C22×C3D3×#4112yes—
759C22×C3C2×C3×#4114yes—
760C22×C3C2×C3×#4112yes—
761C22×C3C2×C3×#4112yes—
762C22×C3C2×C3×#4112yes—
763C22×C3C24×D311yescharacteristic
764C22×C3C25×C311yescharacteristic
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—44no—
769C3×C4—24no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—22no—
773C3×C4—22no—
774C3×C4—22no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—24no—
779C3×C4—34no—
780C3×C4—42no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—62no—
786C3×C4—62no—
787C3×C4—62no—
788C3×C4—62no—
789C3×C4C2×#23714yes—
790C3×C4C2×C3×#4114yes—
791Dic3—22no—
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3—22no—
796Dic3—22no—
797Dic3C2×C3×#4114yes—
798C32C2×#52911yescharacteristic, complemented, Sylow
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—32no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23C3×#23514yes—
809C23C23×C3×D312yes—
810C23C23×C3×D312yes—
811C23C23×C3×D311yescharacteristic
812Q8—68no—
813D4—28no—
814D4—68no—
815D4—68no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—34no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—68no—
831C2×C4—68no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—68no—
839C2×C4C3×#23714yes—
840C2×C4C23×C3×D312yes—
841C2×C4C23×C3×D312yes—
842C2×C4C23×C3×D312yes—
843C2×C4C23×C3×D312yes—
844C2×C4C23×C3×D312yes—
845C2×C3—24no—
846C2×C3—24no—
847C2×C3—24no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—44no—
852C2×C3—44no—
853C2×C3—42no—
854C2×C3—42no—
855C2×C3—122no—
856C2×C3#553814yesdirect product factor
857C2×C3C3×#52914yescomplemented
858C2×C3C22×#23511yescharacteristic
859C2×C3C22×#23711yescharacteristic
860C2×C3C2×D3×#4111yescharacteristic
861C2×C3C22×C3×#4111yescharacteristic
862C2×C3C22×C3×#4111yescharacteristic
863C2×C3C22×C3×#4111yescharacteristic
864D3—42no—
865C22—28no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—124no—
876C22C2×C3×#23514yes—
877C22C2×C3×#23512yes—
878C22C2×C3×#23712yes—
879C22C3×D3×#4112yes—
880C22C24×C3×D311yescharacteristic
881C4—22no—
882C4—22no—
883C4—22no—
884C4—22no—
885C4—34no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—62no—
890C4—62no—
891C4—62no—
892C4C2×C3×#23714yes—
893C3—21no—
894C3C2×#553811yescharacteristic, direct product factor
895C3C2×C3×#52911yescharacteristic, complemented
896C2—24no—
897C2—42no—
898C2—122no—
899C2C3×#553814yesdirect product factor
900C2C22×C3×#23511yescharacteristic
901C2C22×C3×#23711yescharacteristic
902C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#939C2
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#529
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×#935C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C2×C3×#926C2semidirect
7. C22×C3×C4×Dic3C2semidirect
8. C3×#5538C2direct (N × H)
9. C2×C3×#898C2semidirect
10. C2×C3×#889C2semidirect
11. C2×C3×#886C2semidirect
12. C2×C3×#885C2semidirect
13. C2×C3×#879C2semidirect
14. C2×C3×#878C2semidirect
15. C2×C3×#872C2semidirect
16. C2×C3×C4×Dic6C2semidirect
18. C2×#5538C3direct (N × H)
28. C32×C4×D4C22semidirect
38. C3×#935C22semidirect
39. C3×C4×#67C22semidirect
40. C3×C4×#67C22semidirect
45. C3×#926C22semidirect
60. C2×C3×C4×Dic3C22semidirect
61. C3×#898C22semidirect
62. C3×#889C22semidirect
63. C3×#886C22semidirect
64. C3×#885C22semidirect
65. C3×#879C22semidirect
66. C3×#878C22semidirect
67. C3×#872C22semidirect
68. C3×C4×Dic6C22semidirect
82. C2×C3×C4×D4D3semidirect
83. C2×C3×C4×D4C2×C3semidirect
88. C2×#935C2×C3semidirect
89. C2×C4×#67C2×C3semidirect
90. C2×C4×#67C2×C3semidirect
91. C2×#926C2×C3semidirect
92. C22×C4×Dic3C2×C3semidirect
93. #5538C2×C3direct (N × H)
94. C2×#898C2×C3semidirect
95. C2×#889C2×C3semidirect
96. C2×#886C2×C3semidirect
97. C2×#885C2×C3semidirect
98. C2×#879C2×C3semidirect
99. C2×#878C2×C3semidirect
100. C2×#872C2×C3semidirect
101. C2×C4×Dic6C2×C3semidirect
195. C3×C4×D4C2×D3semidirect
196. C3×C4×D4C22×C3semidirect
239. #935C22×C3semidirect
240. C4×#67C22×C3semidirect
241. C4×#67C22×C3semidirect
246. #926C22×C3semidirect
261. C2×C4×Dic3C22×C3semidirect
262. #898C22×C3semidirect
263. #889C22×C3semidirect
264. #886C22×C3semidirect
265. #885C22×C3semidirect
266. #879C22×C3semidirect
267. #878C22×C3semidirect
268. #872C22×C3semidirect
269. C4×Dic6C22×C3semidirect
328. C2×C4×D4C3×D3semidirect
515. C4×D4C2×C3×D3semidirect
661. C2×C32#529semidirect
798. C32C2×#529semidirect
856. C2×C3#5538direct (N × H)
857. C2×C3C3×#529semidirect
894. C3C2×#5538direct (N × H)
895. C3C2×C3×#529semidirect
899. C2C3×#5538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9392
C2×C3×#9352
C2×C3×C4×#672
C2×C3×#9262
C22×C3×C4×Dic32
C3×#55382
C2×C3×#8982
C2×C3×#8892
C2×C3×#8862
C2×C3×#8852
C2×C3×#8792
C2×C3×#8782
C2×C3×#8722
C2×C3×C4×Dic62
C2×C3×#5293
C2×#55383