Finite Group Databasebeta

← C2×C3×#5568 #11903367

Subgroups — C2×C3×#5568 #11903367

Order 1152.

2373 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C3×#5568C2116yesmaximal, direct product factor
5C2×C3×#898C212yesmaximal, complemented
6C2×C3×#896C212yesmaximal, complemented
7C2×C3×#893C211yesmaximal, characteristic
8C2×C3×#887C211yesmaximal, characteristic, complemented
9C2×C3×#876C212yesmaximal, complemented
10C2×C3×#875C211yesmaximal, characteristic
11C2×C3×#872C212yesmaximal, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#556—31nomaximal
14C2×#5568C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C4×Q8C2218yescomplemented
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C4⋊C4C2212yes—
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2212yes—
25C3×#947C2218yes—
26C3×#944C2218yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2212yes—
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#898C22116yescomplemented
42C3×#896C22116yescomplemented
43C3×#893C2218yes—
44C3×#887C2218yescomplemented
45C3×#876C22116yescomplemented
46C3×#875C2218yes—
47C3×#872C22116yescomplemented
48C3×C4×Dic6C2218yescomplemented
49C3×#556—316no—
50C2×C3×C4⋊Q8—31no—
51C2×C3×#126—32no—
52C2×C3×#126—32no—
53C2×C3×#124—31no—
54C2×C3×#124—31no—
55C2×C3×C22⋊Q8—32no—
56C2×C3×C4×Q8—21no—
57C2×C3×C4×Q8—31no—
58C2×C3×C4×Q8—31no—
59C2×C3×C4×Q8D311yescharacteristic, complemented
60C2×C3×C4×Q8C2×C311yescharacteristic, complemented
61C2×C3×C4×D4—31no—
62C2×C3×#117—32no—
63C2×#947C2×C311yescharacteristic
64C2×#944C2×C311yescharacteristic, complemented
65#5568C2×C3116yesdirect product factor
66C2×#898C2×C312yescomplemented
67C2×#896C2×C312yescomplemented
68C2×#893C2×C311yescharacteristic
69C2×#887C2×C311yescharacteristic, complemented
70C2×#876C2×C312yescomplemented
71C2×#875C2×C311yescharacteristic
72C2×#872C2×C312yescomplemented
73C2×C4×Dic6C2×C311yescharacteristic, complemented
74C23×C3×D3C2312yes—
75C2×C32×Q8—24no—
76C2×C32×Q8C2314yes—
77C22×C32×C4C2312yes—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—24no—
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—28no—
90C2×C3×C4×D3C2318yes—
91C2×C3×Dic6—24no—
92C2×C3×Dic6—24no—
93C2×C3×Dic6C2314yes—
94C2×C3×Dic6C2314yes—
95C32×C4⋊C4C2314yes—
96C32×C4⋊C4C2318yes—
97C32×C42C2314yes—
98C32×C42C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×(C2×D3)⋊C4C2318yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2314yes—
109C3×Dic3⋊C4C2314yes—
110C3×C4×Dic3C2318yes—
111C3×C4×Dic3C2314yes—
112C3×C4×Dic3C2314yes—
113C2×#556—31noSylow
114C22×C3×Q8—21no—
115C22×C3×Q8—31no—
116C22×C3×Q8—31no—
117C22×C3×Q8C2×D311yescharacteristic
118C22×C3×Q8C22×C311yescharacteristic
119C22×C3×D4—31no—
120C23×C3×C4—32no—
121C22×D12C22×C311yescharacteristic
122C22×C4×D3C22×C312yes—
123C22×Dic6C22×C311yescharacteristic
124C22×Dic6C22×C311yescharacteristic
125C3×C4⋊Q8—38no—
126C3×#126—316no—
127C3×#126—316no—
128C3×#124—38no—
129C3×#124—38no—
130C3×C22⋊Q8—316no—
131C3×C4×Q8—28no—
132C3×C4×Q8—38no—
133C3×C4×Q8—38no—
134C3×C4×Q8C2×D318yescomplemented
135C3×C4×Q8C22×C318yescomplemented
136C3×C4×D4—38no—
137C3×#117—316no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—22no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—32no—
142C2×C3×C4⋊C4—32no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—32no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C4⋊C4C2×D312yes—
148C2×C3×C4⋊C4C22×C311yescharacteristic
149C2×C3×C4⋊C4C22×C312yes—
150C2×C3×C22⋊C4—32no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—32no—
155C2×C3×C42—22no—
156C2×C3×C42—21no—
157C2×C3×C42—32no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×C3×C42C2×D312yes—
161C2×C3×C42C2×D311yescharacteristic
162C2×C3×C42C22×C311yescharacteristic
163C2×C3×C42C22×C312yes—
164#947C22×C318yes—
165#944C22×C318yescomplemented
166C2×(C2×D3)⋊C4C22×C312yes—
167C2×(C2×D3)⋊C4C22×C312yes—
168C2×(C2×D3)⋊C4C22×C312yes—
169C2×(C2×D3)⋊C4C22×C312yes—
170C2×(C2×D3)⋊C4C22×C312yes—
171C2×C4⋊Dic3C22×C311yescharacteristic
172C2×Dic3⋊C4C22×C311yescharacteristic
173C2×Dic3⋊C4C22×C311yescharacteristic
174C2×Dic3⋊C4C22×C312yes—
175C2×Dic3⋊C4C22×C312yes—
176C2×Dic3⋊C4C22×C312yes—
177C2×C4×Dic3C22×C311yescharacteristic
178C2×C4×Dic3C22×C311yescharacteristic
179C2×C4×Dic3C22×C312yes—
180#898C22×C3116yescomplemented
181#896C22×C3116yescomplemented
182#893C22×C318yes—
183#887C22×C318yescomplemented
184#876C22×C3116yescomplemented
185#875C22×C318yes—
186#872C22×C3116yescomplemented
187C4×Dic6C22×C318yescomplemented
188C23×C32C2411yescharacteristic
189C22×C3×D3—24no—
190C22×C3×D3—24no—
191C22×C3×D3—24no—
192C22×C3×D3C2414yes—
193C32×Q8—28no—
194C2×C32×C4—24no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—24no—
198C2×C32×C4#4114yes—
199C2×C32×C4C2414yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2414yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2412yes—
204C2×C3×Dic3—24no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3#4114yes—
209C2×C3×Dic3C2412yes—
210C2×C3×Dic3C2412yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C2×C3×Dic3C2412yes—
214C3×D12—28no—
215C3×C4×D3—216no—
216C3×Dic6—28no—
217C3×Dic6—28no—
218#556—316no—
219C2×C4⋊Q8—31no—
220C2×#126—32no—
221C2×#126—32no—
222C2×#124—31no—
223C2×#124—31no—
224C2×C22⋊Q8—32no—
225C2×C4×Q8—31no—
226C2×C4×Q8—31no—
227C2×C4×Q8C3×D311yescharacteristic, complemented
228C2×C4×D4—31no—
229C2×#117—32no—
230C24×C3—32no—
231C23×D3C23×C312yes—
232C2×C3×Q8—28no—
233C2×C3×Q8—24no—
234C2×C3×Q8—24no—
235C2×C3×Q8—24no—
236C2×C3×Q8—34no—
237C2×C3×Q8—34no—
238C2×C3×Q8—64no—
239C2×C3×Q8—64no—
240C2×C3×Q8C22×D314yes—
241C2×C3×Q8C23×C314yes—
242C2×C3×D4—34no—
243C2×C3×D4—64no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C22×C3×C4—21no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—32no—
253C22×C3×C4—31no—
254C22×C3×C4—38no—
255C22×C3×C4—68no—
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C23×C312yes—
262C22×C3×C4C23×C311yescharacteristic
263C22×C3×C4C23×C312yes—
264C22×C3×C4C23×C311yescharacteristic
265C22×C3×C4C23×C311yescharacteristic
266C22×Dic3C23×C311yescharacteristic
267C22×Dic3C23×C311yescharacteristic
268C22×Dic3C23×C311yescharacteristic
269C22×Dic3C23×C312yes—
270C22×Dic3C23×C311yescharacteristic
271C2×D12—24no—
272C2×D12C23×C314yes—
273C2×C4×D3—28no—
274C2×C4×D3C23×C318yes—
275C2×Dic6—24no—
276C2×Dic6—24no—
277C2×Dic6C23×C314yes—
278C2×Dic6C23×C314yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—34no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—38no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—38no—
286C3×C4⋊C4—34no—
287C3×C4⋊C4C22×D314yes—
288C3×C4⋊C4C22×D318yes—
289C3×C4⋊C4C23×C314yes—
290C3×C4⋊C4C23×C318yes—
291C3×C22⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C22⋊C4—38no—
296C3×C42—28no—
297C3×C42—24no—
298C3×C42—38no—
299C3×C42—34no—
300C3×C42—34no—
301C3×C42C22×D318yes—
302C3×C42C22×D314yes—
303C3×C42C23×C314yes—
304C3×C42C23×C318yes—
305(C2×D3)⋊C4C23×C318yes—
306(C2×D3)⋊C4C23×C318yes—
307(C2×D3)⋊C4C23×C318yes—
308(C2×D3)⋊C4C23×C318yes—
309(C2×D3)⋊C4C23×C318yes—
310C4⋊Dic3C23×C314yes—
311Dic3⋊C4C23×C314yes—
312Dic3⋊C4C23×C314yes—
313Dic3⋊C4C23×C318yes—
314Dic3⋊C4C23×C318yes—
315Dic3⋊C4C23×C318yes—
316C4×Dic3C23×C314yes—
317C4×Dic3C23×C314yes—
318C4×Dic3C23×C318yes—
319C22×C32C2×#4112yes—
320C22×C32C2×#4112yes—
321C22×C322−1+412yes—
322C22×C32C2511yescharacteristic
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—48no—
327C32×C4—24no—
328C32×C4—22no—
329C32×C4—22no—
330C32×C4—24no—
331C32×C4C2×#4114yes—
332C3×Dic3—24no—
333C3×Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—22no—
336C3×Dic3C2×#4114yes—
337C22×Q8—31no—
338C22×Q8—31no—
339C22×Q8C2×C3×D311yescharacteristic
340C22×D4—31no—
341C23×C4—32no—
342C4⋊Q8—38no—
343#126—316no—
344#126—316no—
345#124—38no—
346#124—38no—
347C22⋊Q8—316no—
348C4×Q8—38no—
349C4×Q8—38no—
350C4×Q8C2×C3×D318yescomplemented
351C4×D4—38no—
352#117—316no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—32no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—32no—
359C2×C4⋊C4C2×C3×D311yescharacteristic
360C2×C4⋊C4C2×C3×D312yes—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—32no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—32no—
366C2×C42—32no—
367C2×C42—31no—
368C2×C42—31no—
369C2×C42C2×C3×D312yes—
370C2×C42C2×C3×D311yescharacteristic
371C23×C3—21no—
372C23×C3—34no—
373C23×C3—64no—
374C23×C3—64no—
375C23×C3—64no—
376C23×C3C23×D311yescharacteristic
377C23×C3C24×C311yescharacteristic
378C22×D3—24no—
379C22×D3—24no—
380C22×D3—24no—
381C22×D3C24×C314yes—
382C3×Q8—216no—
383C3×Q8—28no—
384C3×Q8—28no—
385C3×Q8—68no—
386C3×Q8—68no—
387C3×D4—68no—
388C2×C3×C4—24no—
389C2×C3×C4—28no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—34no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—34no—
409C2×C3×C4—32no—
410C2×C3×C4—44no—
411C2×C3×C4—42no—
412C2×C3×C4—616no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4#23514yes—
418C2×C3×C4C3×#4114yes—
419C2×C3×C4C23×D314yes—
420C2×C3×C4C23×D312yes—
421C2×C3×C4C23×D314yes—
422C2×C3×C4C23×D312yes—
423C2×C3×C4C23×D312yes—
424C2×C3×C4C24×C314yes—
425C2×C3×C4C24×C312yes—
426C2×C3×C4C24×C314yes—
427C2×C3×C4C24×C312yes—
428C2×C3×C4C24×C312yes—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3C3×#4114yes—
434C2×Dic3C24×C312yes—
435C2×Dic3C24×C312yes—
436C2×Dic3C24×C312yes—
437C2×Dic3C24×C314yes—
438C2×Dic3C24×C312yes—
439D12—28no—
440C4×D3—216no—
441Dic6—28no—
442Dic6—28no—
443C2×C32#55614yescomplemented
444C2×C32C22×#4111yescharacteristic
445C2×C32C22×#4111yescharacteristic
446C2×C32C2×2−1+411yescharacteristic
447C3×D3—44no—
448C24—32no—
449C2×Q8—24no—
450C2×Q8—34no—
451C2×Q8—34no—
452C2×Q8—64no—
453C2×Q8—64no—
454C2×Q8C22×C3×D314yes—
455C2×D4—34no—
456C2×D4—64no—
457C22×C4—31no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—32no—
461C22×C4—31no—
462C22×C4—38no—
463C22×C4—68no—
464C22×C4C22×C3×D312yes—
465C22×C4C22×C3×D311yescharacteristic
466C22×C4C22×C3×D312yes—
467C22×C4C22×C3×D311yescharacteristic
468C22×C4C22×C3×D311yescharacteristic
469C4⋊C4—34no—
470C4⋊C4—38no—
471C4⋊C4—38no—
472C4⋊C4—34no—
473C4⋊C4—34no—
474C4⋊C4—38no—
475C4⋊C4C22×C3×D314yes—
476C4⋊C4C22×C3×D318yes—
477C22⋊C4—38no—
478C22⋊C4—38no—
479C22⋊C4—38no—
480C22⋊C4—38no—
481C22⋊C4—38no—
482C42—38no—
483C42—34no—
484C42—34no—
485C42C22×C3×D318yes—
486C42C22×C3×D314yes—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—64no—
492C22×C3—64no—
493C22×C3—64no—
494C22×C3—128no—
495C22×C3C2×#23512yes—
496C22×C3#100712yes—
497C22×C3D3×#4112yes—
498C22×C3C2×C3×#4112yes—
499C22×C3C2×C3×#4112yes—
500C22×C3C3×2−1+412yes—
501C22×C3C24×D311yescharacteristic
502C22×C3C25×C311yescharacteristic
503C2×D3—24no—
504C2×D3—24no—
505C2×D3—24no—
506C2×D3—48no—
507C3×C4—28no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—22no—
511C3×C4—24no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4—22no—
517C3×C4—24no—
518C3×C4—34no—
519C3×C4—44no—
520C3×C4—42no—
521C3×C4—64no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—62no—
525C3×C4C2×#23514yes—
526C3×C4C2×C3×#4114yes—
527Dic3—24no—
528Dic3—22no—
529Dic3—22no—
530Dic3—22no—
531Dic3C2×C3×#4114yes—
532C32C2×#55611yescharacteristic, complemented, Sylow
533C23—34no—
534C23—64no—
535C23—64no—
536C23—64no—
537C23C23×C3×D311yescharacteristic
538Q8—28no—
539Q8—68no—
540Q8—68no—
541D4—68no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—34no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—34no—
551C2×C4—32no—
552C2×C4—616no—
553C2×C4—64no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4C3×#23514yes—
558C2×C4C23×C3×D314yes—
559C2×C4C23×C3×D312yes—
560C2×C4C23×C3×D314yes—
561C2×C4C23×C3×D312yes—
562C2×C4C23×C3×D312yes—
563C2×C3—24no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—124no—
568C2×C3#556814yesdirect product factor
569C2×C3C3×#55614yescomplemented
570C2×C3C22×#23511yescharacteristic
571C2×C3C2×#100711yescharacteristic
572C2×C3C2×D3×#4111yescharacteristic
573C2×C3C22×C3×#4111yescharacteristic
574C2×C3C22×C3×#4111yescharacteristic
575C2×C3C2×C3×2−1+411yescharacteristic
576D3—44no—
577C22—64no—
578C22—64no—
579C22—64no—
580C22—128no—
581C22C2×C3×#23512yes—
582C22C3×#100712yes—
583C22C3×D3×#4112yes—
584C22C24×C3×D311yescharacteristic
585C4—24no—
586C4—22no—
587C4—24no—
588C4—22no—
589C4—34no—
590C4—64no—
591C4—62no—
592C4—62no—
593C4—62no—
594C4C2×C3×#23514yes—
595C3—21no—
596C3C2×#556811yescharacteristic, direct product factor
597C3C2×C3×#55611yescharacteristic, complemented
598C2—124no—
599C2C3×#556814yesdirect product factor
600C2C22×C3×#23511yescharacteristic
601C2C2×C3×#100711yescharacteristic
602C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4×Q8D3
hypocenterC3C2×C3×#556
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C2×C3×#944C2semidirect
4. C3×#5568C2direct (N × H)
5. C2×C3×#898C2semidirect
6. C2×C3×#896C2semidirect
8. C2×C3×#887C2semidirect
9. C2×C3×#876C2semidirect
11. C2×C3×#872C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5568C3direct (N × H)
20. C32×C4×Q8C22semidirect
26. C3×#944C22semidirect
41. C3×#898C22semidirect
42. C3×#896C22semidirect
44. C3×#887C22semidirect
45. C3×#876C22semidirect
47. C3×#872C22semidirect
48. C3×C4×Dic6C22semidirect
59. C2×C3×C4×Q8D3semidirect
60. C2×C3×C4×Q8C2×C3semidirect
64. C2×#944C2×C3semidirect
65. #5568C2×C3direct (N × H)
66. C2×#898C2×C3semidirect
67. C2×#896C2×C3semidirect
69. C2×#887C2×C3semidirect
70. C2×#876C2×C3semidirect
72. C2×#872C2×C3semidirect
73. C2×C4×Dic6C2×C3semidirect
134. C3×C4×Q8C2×D3semidirect
135. C3×C4×Q8C22×C3semidirect
165. #944C22×C3semidirect
180. #898C22×C3semidirect
181. #896C22×C3semidirect
183. #887C22×C3semidirect
184. #876C22×C3semidirect
186. #872C22×C3semidirect
187. C4×Dic6C22×C3semidirect
227. C2×C4×Q8C3×D3semidirect
350. C4×Q8C2×C3×D3semidirect
443. C2×C32#556semidirect
532. C32C2×#556semidirect
568. C2×C3#5568direct (N × H)
569. C2×C3C3×#556semidirect
596. C3C2×#5568direct (N × H)
597. C3C2×C3×#556semidirect
599. C2C3×#5568direct (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×Q82
C2×C3×#9472
C2×C3×#9442
C3×#55682
C2×C3×#8982
C2×C3×#8962
C2×C3×#8932
C2×C3×#8872
C2×C3×#8762
C2×C3×#8752
C2×C3×#8722
C2×C3×C4×Dic62
C2×C3×#5563
C2×#55683