Finite Group Databasebeta

← C2×C3×#5669 #11901610

Subgroups — C2×C3×#5669 #11901610

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic
5C2×C3×#935C211yesmaximal, characteristic, complemented
6C3×#5669C2116yesmaximal, direct product factor
7C2×C3×#885C211yesmaximal, characteristic, complemented
8C2×C3×#885C211yesmaximal, characteristic, complemented
9C2×C3×#883C211yesmaximal, characteristic, complemented
10C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
11C2×C3×#879C211yesmaximal, characteristic, complemented
12C2×C3×#878C211yesmaximal, characteristic, complemented
13C2×C3×#878C211yesmaximal, characteristic, complemented
14C2×C3×#877C211yesmaximal, characteristic, complemented
15C2×C3×#876C211yesmaximal, characteristic, complemented
16C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
17C2×C3×#542—31nomaximal
18C2×#5669C311yesmaximal, characteristic, direct product factor
19C22×C32×Q8C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C32×#124C2218yescomplemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C42C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C3×#946C2218yescomplemented
39C3×#944C2218yescomplemented
40C3×#939C2218yes—
41C3×#935C2218yescomplemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
53C2×C3×Dic3⋊C4C2211yescharacteristic
54C2×C3×Dic3⋊C4C2211yescharacteristic
55C2×C3×Dic3⋊C4C2211yescharacteristic
56C2×C3×C4×Dic3C2211yescharacteristic
57C2×C3×C4×Dic3C2211yescharacteristic
58C2×C3×C4×Dic3C2211yescharacteristic
59C3×#885C2218yescomplemented
60C3×#885C2218yescomplemented
61C3×#883C2218yescomplemented
62C3×#67⋊C4C2218yescomplemented
63C3×#879C2218yescomplemented
64C3×#878C2218yescomplemented
65C3×#878C2218yescomplemented
66C3×#877C2218yescomplemented
67C3×#876C2218yescomplemented
68C3×C4×Dic6C2218yescomplemented
69C3×#542—316no—
70C2×C3×C4⋊Q8—31no—
71C2×C3×#126—31no—
72C2×C3×#126—31no—
73C2×C3×#124—21no—
74C2×C3×#124—31no—
75C2×C3×#124—31no—
76C2×C3×#124D311yescharacteristic, complemented
77C2×C3×#124C2×C311yescharacteristic, complemented
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—
87C2×#946C2×C311yescharacteristic, complemented
88C2×#944C2×C311yescharacteristic, complemented
89C2×#939C2×C311yescharacteristic
90C2×#935C2×C311yescharacteristic, complemented
91#5669C2×C3116yesdirect product factor
92C2×#885C2×C311yescharacteristic, complemented
93C2×#885C2×C311yescharacteristic, complemented
94C2×#883C2×C311yescharacteristic, complemented
95C2×#67⋊C4C2×C311yescharacteristic, complemented
96C2×#879C2×C311yescharacteristic, complemented
97C2×#878C2×C311yescharacteristic, complemented
98C2×#878C2×C311yescharacteristic, complemented
99C2×#877C2×C311yescharacteristic, complemented
100C2×#876C2×C311yescharacteristic, complemented
101C2×C4×Dic6C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C2×C32×Q8—42no—
106C2×C32×Q8C2314yes—
107C2×C32×D4—42no—
108C2×C32×D4C2314yes—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×C3×#67—24no—
115C2×C3×#67—42no—
116C2×C3×#67C2314yes—
117C2×C3×#67C2314yes—
118C22×C3×Dic3—24no—
119C22×C3×Dic3—42no—
120C22×C3×Dic3C2314yes—
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3C2314yes—
131C2×C3×Dic6—24no—
132C2×C3×Dic6—42no—
133C2×C3×Dic6C2314yes—
134C2×C3×Dic6C2314yes—
135C32×C22⋊C4C2314yes—
136C32×C22⋊C4C2314yes—
137C32×C22⋊C4C2314yes—
138C32×C22⋊C4C2314yes—
139C32×C42C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
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×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161C2×#542—31noSylow
162C22×C3×Q8—21no—
163C22×C3×Q8—31no—
164C22×C3×Q8—31no—
165C22×C3×Q8C2×D311yescharacteristic
166C22×C3×Q8C22×C311yescharacteristic
167C22×C3×D4—21no—
168C22×C3×D4—31no—
169C22×C3×D4—31no—
170C22×C3×D4C2×D311yescharacteristic
171C22×C3×D4C22×C311yescharacteristic
172C23×C3×C4—31no—
173C23×C3×C4—31no—
174C23×C3×C4—31no—
175C22×#67C22×C311yescharacteristic
176C22×#67C22×C311yescharacteristic
177C23×Dic3C22×C311yescharacteristic
178C23×Dic3C22×C311yescharacteristic
179C22×C4×D3C22×C311yescharacteristic
180C22×Dic6C22×C311yescharacteristic
181C22×Dic6C22×C311yescharacteristic
182C3×C4⋊Q8—38no—
183C3×#126—38no—
184C3×#126—38no—
185C3×#124—28no—
186C3×#124—38no—
187C3×#124—38no—
188C3×#124C2×D318yescomplemented
189C3×#124C22×C318yescomplemented
190C3×#123—38no—
191C3×#123—38no—
192C3×C22⋊Q8—38no—
193C3×C22⋊Q8—38no—
194C3×C22⋊Q8—38no—
195C3×#121—38no—
196C3×C4×Q8—38no—
197C3×C4×D4—38no—
198C3×#117—38no—
199C2×C3×C4⋊C4—31no—
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×C22⋊C4—21no—
210C2×C3×C22⋊C4—21no—
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⋊C4C2×D311yescharacteristic
224C2×C3×C22⋊C4C2×D311yescharacteristic
225C2×C3×C22⋊C4C22×C311yescharacteristic
226C2×C3×C22⋊C4C22×C311yescharacteristic
227C2×C3×C22⋊C4C22×C311yescharacteristic
228C2×C3×C22⋊C4C22×C311yescharacteristic
229C2×C3×C42—21no—
230C2×C3×C42—31no—
231C2×C3×C42—31no—
232C2×C3×C42—31no—
233C2×C3×C42C2×D311yescharacteristic
234C2×C3×C42C22×C311yescharacteristic
235C2×#217C22×C311yescharacteristic
236C2×#217C22×C311yescharacteristic
237C2×#217C22×C311yescharacteristic
238C2×#217C22×C311yescharacteristic
239#946C22×C318yescomplemented
240#944C22×C318yescomplemented
241#939C22×C318yes—
242#935C22×C318yescomplemented
243C2×(C2×D3)⋊C4C22×C311yescharacteristic
244C2×(C2×D3)⋊C4C22×C311yescharacteristic
245C2×(C2×D3)⋊C4C22×C311yescharacteristic
246C2×(C2×D3)⋊C4C22×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×Dic3⋊C4C22×C311yescharacteristic
254C2×Dic3⋊C4C22×C311yescharacteristic
255C2×Dic3⋊C4C22×C311yescharacteristic
256C2×Dic3⋊C4C22×C311yescharacteristic
257C2×C4×Dic3C22×C311yescharacteristic
258C2×C4×Dic3C22×C311yescharacteristic
259C2×C4×Dic3C22×C311yescharacteristic
260#885C22×C318yescomplemented
261#885C22×C318yescomplemented
262#883C22×C318yescomplemented
263#67⋊C4C22×C318yescomplemented
264#879C22×C318yescomplemented
265#878C22×C318yescomplemented
266#878C22×C318yescomplemented
267#877C22×C318yescomplemented
268#876C22×C318yescomplemented
269C4×Dic6C22×C318yescomplemented
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C32×Q8—44no—
284C32×D4—44no—
285C2×C32×C4—22no—
286C2×C32×C4—22no—
287C2×C32×C4—22no—
288C2×C32×C4—22no—
289C2×C32×C4—22no—
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—22no—
303C2×C3×Dic3—28no—
304C2×C3×Dic3—44no—
305C2×C3×Dic3#4114yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C3×C4×D3—44no—
314C3×Dic6—28no—
315C3×Dic6—44no—
316#542—316no—
317C2×C4⋊Q8—31no—
318C2×#126—31no—
319C2×#126—31no—
320C2×#124—31no—
321C2×#124—31no—
322C2×#124C3×D311yescharacteristic, complemented
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—21no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C24×C3C23×C311yescharacteristic
338C24×C3C23×C311yescharacteristic
339C23×D3C23×C311yescharacteristic
340C2×C3×Q8—24no—
341C2×C3×Q8—34no—
342C2×C3×Q8—34no—
343C2×C3×Q8—42no—
344C2×C3×Q8—42no—
345C2×C3×Q8—44no—
346C2×C3×Q8—64no—
347C2×C3×Q8—122no—
348C2×C3×Q8C22×D314yes—
349C2×C3×Q8C23×C314yes—
350C2×C3×D4—24no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—42no—
354C2×C3×D4—42no—
355C2×C3×D4—44no—
356C2×C3×D4—64no—
357C2×C3×D4—122no—
358C2×C3×D4C22×D314yes—
359C2×C3×D4C23×C314yes—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—31no—
366C22×C3×C4—34no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—34no—
374C22×C3×C4—34no—
375C22×C3×C4—64no—
376C22×C3×C4—122no—
377C22×C3×C4—122no—
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C23×C311yescharacteristic
384C22×C3×C4C23×C311yescharacteristic
385C22×C3×C4C23×C311yescharacteristic
386C22×C3×C4C23×C311yescharacteristic
387C22×C3×C4C23×C311yescharacteristic
388C2×#67—24no—
389C2×#67—42no—
390C2×#67C23×C314yes—
391C2×#67C23×C314yes—
392C22×Dic3—24no—
393C22×Dic3—42no—
394C22×Dic3C23×C314yes—
395C22×Dic3C23×C311yescharacteristic
396C22×Dic3C23×C311yescharacteristic
397C22×Dic3C23×C311yescharacteristic
398C22×Dic3C23×C311yescharacteristic
399C22×Dic3C23×C311yescharacteristic
400C22×Dic3C23×C311yescharacteristic
401C22×Dic3C23×C314yes—
402C22×Dic3C23×C311yescharacteristic
403C2×C4×D3—42no—
404C2×C4×D3C23×C314yes—
405C2×Dic6—24no—
406C2×Dic6—42no—
407C2×Dic6C23×C314yes—
408C2×Dic6C23×C314yes—
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⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C22⋊C4—24no—
420C3×C22⋊C4—24no—
421C3×C22⋊C4—24no—
422C3×C22⋊C4—24no—
423C3×C22⋊C4—34no—
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⋊C4C22×D314yes—
432C3×C22⋊C4C22×D314yes—
433C3×C22⋊C4C22×D314yes—
434C3×C22⋊C4C22×D314yes—
435C3×C22⋊C4C23×C314yes—
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#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—
455Dic3⋊C4C23×C314yes—
456Dic3⋊C4C23×C314yes—
457Dic3⋊C4C23×C314yes—
458Dic3⋊C4C23×C314yes—
459Dic3⋊C4C23×C314yes—
460Dic3⋊C4C23×C314yes—
461Dic3⋊C4C23×C314yes—
462Dic3⋊C4C23×C314yes—
463C4×Dic3C23×C314yes—
464C4×Dic3C23×C314yes—
465C4×Dic3C23×C314yes—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32C2×#4112yes—
475C22×C32H(5,𝔽2)12yes—
476C22×C322−1+412yes—
477C22×C32C2511yescharacteristic
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—44no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C32×C4—22no—
486C32×C4—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C2×#4114yes—
494C22×Q8—31no—
495C22×Q8—31no—
496C22×Q8C2×C3×D311yescharacteristic
497C22×D4—31no—
498C22×D4—31no—
499C22×D4C2×C3×D311yescharacteristic
500C23×C4—31no—
501C23×C4—31no—
502C23×C4—31no—
503C4⋊Q8—38no—
504#126—38no—
505#126—38no—
506#124—38no—
507#124—38no—
508#124C2×C3×D318yescomplemented
509#123—38no—
510#123—38no—
511C22⋊Q8—38no—
512C22⋊Q8—38no—
513C22⋊Q8—38no—
514#121—38no—
515C4×Q8—38no—
516C4×D4—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⋊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⋊C4—31no—
536C2×C22⋊C4C2×C3×D311yescharacteristic
537C2×C22⋊C4C2×C3×D311yescharacteristic
538C2×C22⋊C4C2×C3×D311yescharacteristic
539C2×C22⋊C4C2×C3×D311yescharacteristic
540C2×C42—31no—
541C2×C42—31no—
542C2×C42—31no—
543C2×C42C2×C3×D311yescharacteristic
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
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—32no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3C23×D312yes—
570C23×C3C23×D312yes—
571C23×C3C23×D311yescharacteristic
572C23×C3C24×C312yes—
573C23×C3C24×C312yes—
574C23×C3C24×C311yescharacteristic
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3C24×C312yes—
579C3×Q8—44no—
580C3×Q8—44no—
581C3×Q8—48no—
582C3×Q8—68no—
583C3×Q8—124no—
584C3×D4—44no—
585C3×D4—44no—
586C3×D4—48no—
587C3×D4—68no—
588C3×D4—124no—
589C2×C3×C4—24no—
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—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
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—42no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—68no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—124no—
625C2×C3×C4—124no—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C24×C312yes—
632C2×C3×C4C24×C312yes—
633C2×C3×C4C24×C312yes—
634C2×C3×C4C24×C312yes—
635C2×C3×C4C24×C312yes—
636#67—28no—
637#67—44no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—28no—
645C2×Dic3—44no—
646C2×Dic3C3×#4114yes—
647C2×Dic3C24×C312yes—
648C2×Dic3C24×C312yes—
649C2×Dic3C24×C312yes—
650C2×Dic3C24×C312yes—
651C2×Dic3C24×C312yes—
652C2×Dic3C24×C312yes—
653C2×Dic3C24×C312yes—
654C4×D3—44no—
655Dic6—28no—
656Dic6—44no—
657C2×C32—42no—
658C2×C32—42no—
659C2×C32#54214yescomplemented
660C2×C32C22×#4111yescharacteristic
661C2×C32C2×H(5,𝔽2)11yescharacteristic
662C2×C32C2×2−1+411yescharacteristic
663C3×D3—42no—
664C24—31no—
665C24C22×C3×D311yescharacteristic
666C24C22×C3×D311yescharacteristic
667C2×Q8—34no—
668C2×Q8—34no—
669C2×Q8—42no—
670C2×Q8—64no—
671C2×Q8—122no—
672C2×Q8C22×C3×D314yes—
673C2×D4—34no—
674C2×D4—34no—
675C2×D4—42no—
676C2×D4—64no—
677C2×D4—122no—
678C2×D4C22×C3×D314yes—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—34no—
687C22×C4—34no—
688C22×C4—34no—
689C22×C4—64no—
690C22×C4—122no—
691C22×C4—122no—
692C22×C4C22×C3×D311yescharacteristic
693C22×C4C22×C3×D311yescharacteristic
694C22×C4C22×C3×D311yescharacteristic
695C22×C4C22×C3×D311yescharacteristic
696C22×C4C22×C3×D311yescharacteristic
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—34no—
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4C22×C3×D314yes—
716C22⋊C4C22×C3×D314yes—
717C22⋊C4C22×C3×D314yes—
718C22⋊C4C22×C3×D314yes—
719C42—34no—
720C42—34no—
721C42—34no—
722C42C22×C3×D314yes—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—44no—
746C22×C3—44no—
747C22×C3—44no—
748C22×C3—44no—
749C22×C3—62no—
750C22×C3—62no—
751C22×C3—62no—
752C22×C3—84no—
753C22×C3—84no—
754C22×C3—124no—
755C22×C3#100412yes—
756C22×C3D3×#4112yes—
757C22×C3#101012yes—
758C22×C3C2×C3×#4112yes—
759C22×C3C3×H(5,𝔽2)12yes—
760C22×C3C3×2−1+412yes—
761C22×C3C24×D311yescharacteristic
762C22×C3C25×C311yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—44no—
767C3×C4—24no—
768C3×C4—22no—
769C3×C4—22no—
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—34no—
779C3×C4—42no—
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—
789Dic3—22no—
790Dic3—22no—
791Dic3—22no—
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3C2×C3×#4114yes—
796C32C2×#54211yescharacteristic, complemented, Sylow
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—32no—
804C23—62no—
805C23—62no—
806C23—62no—
807C23C23×C3×D312yes—
808C23C23×C3×D312yes—
809C23C23×C3×D311yescharacteristic
810Q8—44no—
811Q8—68no—
812Q8—124no—
813D4—44no—
814D4—68no—
815D4—124no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—34no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—68no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—124no—
837C2×C4—124no—
838C2×C4C23×C3×D312yes—
839C2×C4C23×C3×D312yes—
840C2×C4C23×C3×D312yes—
841C2×C4C23×C3×D312yes—
842C2×C4C23×C3×D312yes—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—24no—
847C2×C3—42no—
848C2×C3—42no—
849C2×C3—42no—
850C2×C3—42no—
851C2×C3—82no—
852C2×C3—82no—
853C2×C3—122no—
854C2×C3#566914yesdirect product factor
855C2×C3C3×#54214yescomplemented
856C2×C3C2×#100411yescharacteristic
857C2×C3C2×D3×#4111yescharacteristic
858C2×C3C2×#101011yescharacteristic
859C2×C3C22×C3×#4111yescharacteristic
860C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
861C2×C3C2×C3×2−1+411yescharacteristic
862D3—42no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—44no—
870C22—44no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—124no—
875C22C3×#100412yes—
876C22C3×D3×#4112yes—
877C22C3×#101012yes—
878C22C24×C3×D311yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—34no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—62no—
890C4—62no—
891C3—21no—
892C3C2×#566911yescharacteristic, direct product factor
893C3C2×C3×#54211yescharacteristic, complemented
894C2—42no—
895C2—42no—
896C2—122no—
897C2C3×#566914yesdirect product factor
898C2C2×C3×#100411yescharacteristic
899C2C2×C3×D3×#4111yescharacteristic
900C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#124C2
socleC23×C32C24
prime radicalC2×C3×#939C2
hypercenterC2×C3×#124D3
hypocenterC3C2×C3×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#124

Complements

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

NH ≅ G/Ntype
1. C2×C32×#124C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×#944C2semidirect
5. C2×C3×#935C2semidirect
6. C3×#5669C2direct (N × H)
7. C2×C3×#885C2semidirect
8. C2×C3×#885C2semidirect
9. C2×C3×#883C2semidirect
10. C2×C3×#67⋊C4C2semidirect
11. C2×C3×#879C2semidirect
12. C2×C3×#878C2semidirect
13. C2×C3×#878C2semidirect
14. C2×C3×#877C2semidirect
15. C2×C3×#876C2semidirect
16. C2×C3×C4×Dic6C2semidirect
18. C2×#5669C3direct (N × H)
28. C32×#124C22semidirect
38. C3×#946C22semidirect
39. C3×#944C22semidirect
41. C3×#935C22semidirect
59. C3×#885C22semidirect
60. C3×#885C22semidirect
61. C3×#883C22semidirect
62. C3×#67⋊C4C22semidirect
63. C3×#879C22semidirect
64. C3×#878C22semidirect
65. C3×#878C22semidirect
66. C3×#877C22semidirect
67. C3×#876C22semidirect
68. C3×C4×Dic6C22semidirect
76. C2×C3×#124D3semidirect
77. C2×C3×#124C2×C3semidirect
87. C2×#946C2×C3semidirect
88. C2×#944C2×C3semidirect
90. C2×#935C2×C3semidirect
91. #5669C2×C3direct (N × H)
92. C2×#885C2×C3semidirect
93. C2×#885C2×C3semidirect
94. C2×#883C2×C3semidirect
95. C2×#67⋊C4C2×C3semidirect
96. C2×#879C2×C3semidirect
97. C2×#878C2×C3semidirect
98. C2×#878C2×C3semidirect
99. C2×#877C2×C3semidirect
100. C2×#876C2×C3semidirect
101. C2×C4×Dic6C2×C3semidirect
188. C3×#124C2×D3semidirect
189. C3×#124C22×C3semidirect
239. #946C22×C3semidirect
240. #944C22×C3semidirect
242. #935C22×C3semidirect
260. #885C22×C3semidirect
261. #885C22×C3semidirect
262. #883C22×C3semidirect
263. #67⋊C4C22×C3semidirect
264. #879C22×C3semidirect
265. #878C22×C3semidirect
266. #878C22×C3semidirect
267. #877C22×C3semidirect
268. #876C22×C3semidirect
269. C4×Dic6C22×C3semidirect
322. C2×#124C3×D3semidirect
508. #124C2×C3×D3semidirect
659. C2×C32#542semidirect
796. C32C2×#542semidirect
854. C2×C3#5669direct (N × H)
855. C2×C3C3×#542semidirect
892. C3C2×#5669direct (N × H)
893. C3C2×C3×#542semidirect
897. C2C3×#5669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1242
C2×C3×#9462
C2×C3×#9442
C2×C3×#9392
C2×C3×#9352
C3×#56692
C2×C3×#8852
C2×C3×#8832
C2×C3×#67⋊C42
C2×C3×#8792
C2×C3×#8782
C2×C3×#8772
C2×C3×#8762
C2×C3×C4×Dic62
C2×C3×#5423
C2×#56693