Finite Group Databasebeta

← C2×C3×#5702 #11903352

Subgroups — C2×C3×#5702 #11903352

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C3×#5702C2116yesmaximal, direct product factor
3C2×C3×#898C211yesmaximal, characteristic, complemented
4C2×C3×#898C211yesmaximal, characteristic, complemented
5C2×C3×#896C211yesmaximal, characteristic, complemented
6C2×C3×#888C211yesmaximal, characteristic, complemented
7C2×C3×#887C211yesmaximal, characteristic, complemented
8C2×C3×#887C211yesmaximal, characteristic, complemented
9C2×C3×#885C211yesmaximal, characteristic
10C2×C3×#885C211yesmaximal, characteristic
11C2×C3×#67⋊C4C211yesmaximal, characteristic
12C2×C3×#879C211yesmaximal, characteristic, complemented
13C2×C3×#878C211yesmaximal, characteristic, complemented
14C2×C3×#877C211yesmaximal, characteristic, complemented
15C2×C3×#872C211yesmaximal, characteristic, complemented
16C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
17C2×C3×#556—31nomaximal
18C2×#5702C311yesmaximal, characteristic, direct product factor
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C32×#126C2218yescomplemented
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C42C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×C4×Dic3C2211yescharacteristic
50C2×C3×C4×Dic3C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C2×C3×C4×Dic3C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55C3×#898C2218yescomplemented
56C3×#898C2218yescomplemented
57C3×#896C2218yescomplemented
58C3×#888C2218yescomplemented
59C3×#887C2218yescomplemented
60C3×#887C2218yescomplemented
61C3×#885C2218yes—
62C3×#885C2218yes—
63C3×#67⋊C4C2218yes—
64C3×#879C2218yescomplemented
65C3×#878C2218yescomplemented
66C3×#877C2218yescomplemented
67C3×#872C2218yescomplemented
68C3×C4×Dic6C2218yescomplemented
69C3×#556—316no—
70C2×C3×C4⋊Q8—31no—
71C2×C3×#126—21no—
72C2×C3×#126—31no—
73C2×C3×#126—31no—
74C2×C3×#126—31no—
75C2×C3×#126D311yescharacteristic, complemented
76C2×C3×#126C2×C311yescharacteristic, complemented
77C2×C3×#124—31no—
78C2×C3×#124—31no—
79C2×C3×C22⋊Q8—31no—
80C2×C3×C22⋊Q8—31no—
81C2×C3×C4×Q8—31no—
82C2×C3×C4×Q8—31no—
83C2×C3×C4×Q8—31no—
84C2×C3×C4×D4—31no—
85C2×C3×#117—31no—
86C2×C3×#117—31no—
87#5702C2×C3116yesdirect product factor
88C2×#898C2×C311yescharacteristic, complemented
89C2×#898C2×C311yescharacteristic, complemented
90C2×#896C2×C311yescharacteristic, complemented
91C2×#888C2×C311yescharacteristic, complemented
92C2×#887C2×C311yescharacteristic, complemented
93C2×#887C2×C311yescharacteristic, complemented
94C2×#885C2×C311yescharacteristic
95C2×#885C2×C311yescharacteristic
96C2×#67⋊C4C2×C311yescharacteristic
97C2×#879C2×C311yescharacteristic, complemented
98C2×#878C2×C311yescharacteristic, complemented
99C2×#877C2×C311yescharacteristic, complemented
100C2×#872C2×C311yescharacteristic, complemented
101C2×C4×Dic6C2×C311yescharacteristic, complemented
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×C3×#67—24no—
111C2×C3×#67C2314yes—
112C22×C3×Dic3—24no—
113C22×C3×Dic3C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×C4×D3—24no—
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6—24no—
124C2×C3×Dic6—24no—
125C2×C3×Dic6—24no—
126C2×C3×Dic6C2314yes—
127C2×C3×Dic6C2314yes—
128C2×C3×Dic6C2314yes—
129C32×C4⋊C4C2314yes—
130C32×C4⋊C4C2314yes—
131C32×C4⋊C4C2314yes—
132C32×C22⋊C4C2314yes—
133C32×C22⋊C4C2314yes—
134C32×C22⋊C4C2314yes—
135C32×C42C2314yes—
136C3×#217C2314yes—
137C3×#217C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×C4×Dic3C2314yes—
153C3×C4×Dic3C2314yes—
154C3×C4×Dic3C2314yes—
155C3×C4×Dic3C2314yes—
156C3×C4×Dic3C2314yes—
157C3×C4×Dic3C2314yes—
158C2×#556—31noSylow
159C22×C3×Q8—31no—
160C22×C3×Q8—31no—
161C22×C3×Q8—31no—
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C22×#67C22×C311yescharacteristic
166C23×Dic3C22×C311yescharacteristic
167C22×C4×D3C22×C311yescharacteristic
168C22×Dic6C22×C311yescharacteristic
169C22×Dic6C22×C311yescharacteristic
170C22×Dic6C22×C311yescharacteristic
171C3×C4⋊Q8—38no—
172C3×#126—28no—
173C3×#126—38no—
174C3×#126—38no—
175C3×#126—38no—
176C3×#126C2×D318yescomplemented
177C3×#126C22×C318yescomplemented
178C3×#124—38no—
179C3×#124—38no—
180C3×C22⋊Q8—38no—
181C3×C22⋊Q8—38no—
182C3×C4×Q8—38no—
183C3×C4×Q8—38no—
184C3×C4×Q8—38no—
185C3×C4×D4—38no—
186C3×#117—38no—
187C3×#117—38no—
188C2×C3×C4⋊C4—21no—
189C2×C3×C4⋊C4—21no—
190C2×C3×C4⋊C4—21no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—31no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4C2×D311yescharacteristic
201C2×C3×C4⋊C4C2×D311yescharacteristic
202C2×C3×C4⋊C4C2×D311yescharacteristic
203C2×C3×C4⋊C4C22×C311yescharacteristic
204C2×C3×C4⋊C4C22×C311yescharacteristic
205C2×C3×C4⋊C4C22×C311yescharacteristic
206C2×C3×C22⋊C4—21no—
207C2×C3×C22⋊C4—21no—
208C2×C3×C22⋊C4—21no—
209C2×C3×C22⋊C4—31no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4C2×D311yescharacteristic
217C2×C3×C22⋊C4C2×D311yescharacteristic
218C2×C3×C22⋊C4C2×D311yescharacteristic
219C2×C3×C22⋊C4C22×C311yescharacteristic
220C2×C3×C22⋊C4C22×C311yescharacteristic
221C2×C3×C22⋊C4C22×C311yescharacteristic
222C2×C3×C42—21no—
223C2×C3×C42—31no—
224C2×C3×C42—31no—
225C2×C3×C42—31no—
226C2×C3×C42—31no—
227C2×C3×C42—31no—
228C2×C3×C42—31no—
229C2×C3×C42C2×D311yescharacteristic
230C2×C3×C42C22×C311yescharacteristic
231C2×#217C22×C311yescharacteristic
232C2×#217C22×C311yescharacteristic
233C2×(C2×D3)⋊C4C22×C311yescharacteristic
234C2×(C2×D3)⋊C4C22×C311yescharacteristic
235C2×(C2×D3)⋊C4C22×C311yescharacteristic
236C2×(C2×D3)⋊C4C22×C311yescharacteristic
237C2×(C2×D3)⋊C4C22×C311yescharacteristic
238C2×C4⋊Dic3C22×C311yescharacteristic
239C2×C4⋊Dic3C22×C311yescharacteristic
240C2×Dic3⋊C4C22×C311yescharacteristic
241C2×Dic3⋊C4C22×C311yescharacteristic
242C2×Dic3⋊C4C22×C311yescharacteristic
243C2×Dic3⋊C4C22×C311yescharacteristic
244C2×Dic3⋊C4C22×C311yescharacteristic
245C2×Dic3⋊C4C22×C311yescharacteristic
246C2×Dic3⋊C4C22×C311yescharacteristic
247C2×C4×Dic3C22×C311yescharacteristic
248C2×C4×Dic3C22×C311yescharacteristic
249C2×C4×Dic3C22×C311yescharacteristic
250C2×C4×Dic3C22×C311yescharacteristic
251C2×C4×Dic3C22×C311yescharacteristic
252C2×C4×Dic3C22×C311yescharacteristic
253#898C22×C318yescomplemented
254#898C22×C318yescomplemented
255#896C22×C318yescomplemented
256#888C22×C318yescomplemented
257#887C22×C318yescomplemented
258#887C22×C318yescomplemented
259#885C22×C318yes—
260#885C22×C318yes—
261#67⋊C4C22×C318yes—
262#879C22×C318yescomplemented
263#878C22×C318yescomplemented
264#877C22×C318yescomplemented
265#872C22×C318yescomplemented
266C4×Dic6C22×C318yescomplemented
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—22no—
270C23×C32C2412yes—
271C23×C32C2411yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4—22no—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4C2412yes—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C3×#67—28no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—28no—
295C2×C3×Dic3#4114yes—
296C2×C3×Dic3#4114yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C3×C4×D3—28no—
305C3×Dic6—28no—
306C3×Dic6—28no—
307C3×Dic6—28no—
308#556—316no—
309C2×C4⋊Q8—31no—
310C2×#126—31no—
311C2×#126—31no—
312C2×#126—31no—
313C2×#126C3×D311yescharacteristic, complemented
314C2×#124—31no—
315C2×#124—31no—
316C2×C22⋊Q8—31no—
317C2×C22⋊Q8—31no—
318C2×C4×Q8—31no—
319C2×C4×Q8—31no—
320C2×C4×Q8—31no—
321C2×C4×D4—31no—
322C2×#117—31no—
323C2×#117—31no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C23×C311yescharacteristic
328C23×D3C23×C311yescharacteristic
329C2×C3×Q8—34no—
330C2×C3×Q8—34no—
331C2×C3×Q8—34no—
332C2×C3×Q8—64no—
333C2×C3×Q8—64no—
334C2×C3×Q8—64no—
335C2×C3×D4—34no—
336C2×C3×D4—64no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—34no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—64no—
353C22×C3×C4—64no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C22×C3×C4C23×C311yescharacteristic
362C22×C3×C4C23×C311yescharacteristic
363C22×C3×C4C23×C311yescharacteristic
364C22×C3×C4C23×C311yescharacteristic
365C22×C3×C4C23×C311yescharacteristic
366C2×#67—24no—
367C2×#67C23×C314yes—
368C22×Dic3—24no—
369C22×Dic3C23×C314yes—
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C22×Dic3C23×C311yescharacteristic
373C22×Dic3C23×C311yescharacteristic
374C22×Dic3C23×C311yescharacteristic
375C22×Dic3C23×C311yescharacteristic
376C22×Dic3C23×C311yescharacteristic
377C2×C4×D3—24no—
378C2×C4×D3C23×C314yes—
379C2×Dic6—24no—
380C2×Dic6—24no—
381C2×Dic6—24no—
382C2×Dic6C23×C314yes—
383C2×Dic6C23×C314yes—
384C2×Dic6C23×C314yes—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4—24no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4C22×D314yes—
398C3×C4⋊C4C22×D314yes—
399C3×C4⋊C4C22×D314yes—
400C3×C4⋊C4C23×C314yes—
401C3×C4⋊C4C23×C314yes—
402C3×C4⋊C4C23×C314yes—
403C3×C22⋊C4—24no—
404C3×C22⋊C4—24no—
405C3×C22⋊C4—24no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4C22×D314yes—
414C3×C22⋊C4C22×D314yes—
415C3×C22⋊C4C22×D314yes—
416C3×C22⋊C4C23×C314yes—
417C3×C22⋊C4C23×C314yes—
418C3×C22⋊C4C23×C314yes—
419C3×C42—24no—
420C3×C42—34no—
421C3×C42—34no—
422C3×C42—34no—
423C3×C42—34no—
424C3×C42—34no—
425C3×C42—34no—
426C3×C42C22×D314yes—
427C3×C42C23×C314yes—
428#217C23×C314yes—
429#217C23×C314yes—
430(C2×D3)⋊C4C23×C314yes—
431(C2×D3)⋊C4C23×C314yes—
432(C2×D3)⋊C4C23×C314yes—
433(C2×D3)⋊C4C23×C314yes—
434(C2×D3)⋊C4C23×C314yes—
435C4⋊Dic3C23×C314yes—
436C4⋊Dic3C23×C314yes—
437Dic3⋊C4C23×C314yes—
438Dic3⋊C4C23×C314yes—
439Dic3⋊C4C23×C314yes—
440Dic3⋊C4C23×C314yes—
441Dic3⋊C4C23×C314yes—
442Dic3⋊C4C23×C314yes—
443Dic3⋊C4C23×C314yes—
444C4×Dic3C23×C314yes—
445C4×Dic3C23×C314yes—
446C4×Dic3C23×C314yes—
447C4×Dic3C23×C314yes—
448C4×Dic3C23×C314yes—
449C4×Dic3C23×C314yes—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—22no—
453C22×C32—44no—
454C22×C32C2×#4112yes—
455C22×C32C2×#4112yes—
456C22×C322−1+412yes—
457C22×C32C2511yescharacteristic
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—44no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3C2×#4114yes—
474C3×Dic3C2×#4114yes—
475C22×Q8—31no—
476C22×Q8—31no—
477C22×Q8—31no—
478C22×D4—31no—
479C23×C4—31no—
480C23×C4—31no—
481C4⋊Q8—38no—
482#126—38no—
483#126—38no—
484#126—38no—
485#126C2×C3×D318yescomplemented
486#124—38no—
487#124—38no—
488C22⋊Q8—38no—
489C22⋊Q8—38no—
490C4×Q8—38no—
491C4×Q8—38no—
492C4×Q8—38no—
493C4×D4—38no—
494#117—38no—
495#117—38no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—31no—
505C2×C4⋊C4C2×C3×D311yescharacteristic
506C2×C4⋊C4C2×C3×D311yescharacteristic
507C2×C4⋊C4C2×C3×D311yescharacteristic
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4C2×C3×D311yescharacteristic
516C2×C22⋊C4C2×C3×D311yescharacteristic
517C2×C22⋊C4C2×C3×D311yescharacteristic
518C2×C42—31no—
519C2×C42—31no—
520C2×C42—31no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42C2×C3×D311yescharacteristic
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—32no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3C23×D312yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C24×C312yes—
543C23×C3C24×C311yescharacteristic
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3C24×C312yes—
548C3×Q8—68no—
549C3×Q8—68no—
550C3×Q8—68no—
551C3×D4—68no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—34no—
571C2×C3×C4—34no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—42no—
580C2×C3×C4—42no—
581C2×C3×C4—42no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—68no—
586C2×C3×C4—68no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D312yes—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C24×C312yes—
599C2×C3×C4C24×C312yes—
600C2×C3×C4C24×C312yes—
601C2×C3×C4C24×C312yes—
602C2×C3×C4C24×C312yes—
603C2×C3×C4C24×C312yes—
604#67—28no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—28no—
611C2×Dic3C3×#4114yes—
612C2×Dic3C3×#4114yes—
613C2×Dic3C24×C312yes—
614C2×Dic3C24×C312yes—
615C2×Dic3C24×C312yes—
616C2×Dic3C24×C312yes—
617C2×Dic3C24×C312yes—
618C2×Dic3C24×C312yes—
619C2×Dic3C24×C312yes—
620C4×D3—28no—
621Dic6—28no—
622Dic6—28no—
623Dic6—28no—
624C2×C32—42no—
625C2×C32#55614yescomplemented
626C2×C32C22×#4111yescharacteristic
627C2×C32C22×#4111yescharacteristic
628C2×C32C2×2−1+411yescharacteristic
629C3×D3—42no—
630C24—31no—
631C24C22×C3×D311yescharacteristic
632C2×Q8—34no—
633C2×Q8—34no—
634C2×Q8—34no—
635C2×Q8—64no—
636C2×Q8—64no—
637C2×Q8—64no—
638C2×D4—34no—
639C2×D4—64no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—34no—
648C22×C4—34no—
649C22×C4—64no—
650C22×C4—64no—
651C22×C4C22×C3×D311yescharacteristic
652C22×C4C22×C3×D311yescharacteristic
653C22×C4C22×C3×D311yescharacteristic
654C22×C4C22×C3×D311yescharacteristic
655C22×C4C22×C3×D311yescharacteristic
656C22×C4C22×C3×D311yescharacteristic
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4C22×C3×D314yes—
667C4⋊C4C22×C3×D314yes—
668C4⋊C4C22×C3×D314yes—
669C22⋊C4—34no—
670C22⋊C4—34no—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4C22×C3×D314yes—
677C22⋊C4C22×C3×D314yes—
678C22⋊C4C22×C3×D314yes—
679C42—34no—
680C42—34no—
681C42—34no—
682C42—34no—
683C42—34no—
684C42—34no—
685C42C22×C3×D314yes—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—44no—
700C22×C3—44no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—84no—
705C22×C3—124no—
706C22×C3D3×#4112yes—
707C22×C3D3×#4112yes—
708C22×C3#101012yes—
709C22×C3C2×C3×#4112yes—
710C22×C3C2×C3×#4112yes—
711C22×C3C3×2−1+412yes—
712C22×C3C24×D311yescharacteristic
713C22×C3C25×C311yescharacteristic
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—44no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—34no—
731C3×C4—34no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—42no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—62no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3C2×C3×#4114yes—
749Dic3C2×C3×#4114yes—
750C32C2×#55611yescharacteristic, complemented, Sylow
751C23—22no—
752C23—22no—
753C23—22no—
754C23—32no—
755C23—62no—
756C23—62no—
757C23—62no—
758C23C23×C3×D312yes—
759C23C23×C3×D311yescharacteristic
760Q8—68no—
761Q8—68no—
762Q8—68no—
763D4—68no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—34no—
771C2×C4—34no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—68no—
780C2×C4—68no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4C23×C3×D312yes—
787C2×C4C23×C3×D312yes—
788C2×C4C23×C3×D312yes—
789C2×C4C23×C3×D312yes—
790C2×C4C23×C3×D312yes—
791C2×C4C23×C3×D312yes—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—24no—
796C2×C3—42no—
797C2×C3—42no—
798C2×C3—82no—
799C2×C3—122no—
800C2×C3#570214yesdirect product factor
801C2×C3C3×#55614yescomplemented
802C2×C3C2×D3×#4111yescharacteristic
803C2×C3C2×D3×#4111yescharacteristic
804C2×C3C2×#101011yescharacteristic
805C2×C3C22×C3×#4111yescharacteristic
806C2×C3C22×C3×#4111yescharacteristic
807C2×C3C2×C3×2−1+411yescharacteristic
808D3—42no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—124no—
817C22C3×D3×#4112yes—
818C22C3×D3×#4112yes—
819C22C3×#101012yes—
820C22C24×C3×D311yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—34no—
828C4—34no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—62no—
834C3—21no—
835C3C2×#570211yescharacteristic, direct product factor
836C3C2×C3×#55611yescharacteristic, complemented
837C2—42no—
838C2—122no—
839C2C3×#570214yesdirect product factor
840C2C2×C3×D3×#4111yescharacteristic
841C2C2×C3×D3×#4111yescharacteristic
842C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#126C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×#126D3
hypocenterC3C2×C3×#556
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×#5702C2direct (N × H)
3. C2×C3×#898C2semidirect
4. C2×C3×#898C2semidirect
5. C2×C3×#896C2semidirect
6. C2×C3×#888C2semidirect
7. C2×C3×#887C2semidirect
8. C2×C3×#887C2semidirect
12. C2×C3×#879C2semidirect
13. C2×C3×#878C2semidirect
14. C2×C3×#877C2semidirect
15. C2×C3×#872C2semidirect
16. C2×C3×C4×Dic6C2semidirect
18. C2×#5702C3direct (N × H)
25. C32×#126C22semidirect
55. C3×#898C22semidirect
56. C3×#898C22semidirect
57. C3×#896C22semidirect
58. C3×#888C22semidirect
59. C3×#887C22semidirect
60. C3×#887C22semidirect
64. C3×#879C22semidirect
65. C3×#878C22semidirect
66. C3×#877C22semidirect
67. C3×#872C22semidirect
68. C3×C4×Dic6C22semidirect
75. C2×C3×#126D3semidirect
76. C2×C3×#126C2×C3semidirect
87. #5702C2×C3direct (N × H)
88. C2×#898C2×C3semidirect
89. C2×#898C2×C3semidirect
90. C2×#896C2×C3semidirect
91. C2×#888C2×C3semidirect
92. C2×#887C2×C3semidirect
93. C2×#887C2×C3semidirect
97. C2×#879C2×C3semidirect
98. C2×#878C2×C3semidirect
99. C2×#877C2×C3semidirect
100. C2×#872C2×C3semidirect
101. C2×C4×Dic6C2×C3semidirect
176. C3×#126C2×D3semidirect
177. C3×#126C22×C3semidirect
253. #898C22×C3semidirect
254. #898C22×C3semidirect
255. #896C22×C3semidirect
256. #888C22×C3semidirect
257. #887C22×C3semidirect
258. #887C22×C3semidirect
262. #879C22×C3semidirect
263. #878C22×C3semidirect
264. #877C22×C3semidirect
265. #872C22×C3semidirect
266. C4×Dic6C22×C3semidirect
313. C2×#126C3×D3semidirect
485. #126C2×C3×D3semidirect
625. C2×C32#556semidirect
750. C32C2×#556semidirect
800. C2×C3#5702direct (N × H)
801. C2×C3C3×#556semidirect
835. C3C2×#5702direct (N × H)
836. C3C2×C3×#556semidirect
839. C2C3×#5702direct (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×#57022
C2×C3×#8982
C2×C3×#8962
C2×C3×#8882
C2×C3×#8872
C2×C3×#8852
C2×C3×#67⋊C42
C2×C3×#8792
C2×C3×#8782
C2×C3×#8772
C2×C3×#8722
C2×C3×C4×Dic62
C2×C3×#5563
C2×#57023