Finite Group Databasebeta

← C3×#17578 #10636185

Subgroups — C3×#17578 #10636185

Order 768.

1418 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#407C211yesmaximal, characteristic
3C3×#2280C211yesmaximal, characteristic
4C3×#1520C214yesmaximal, complemented
5C3×#1511C214yesmaximal, complemented
6C3×#1508C214yesmaximal, complemented
7#17578C311yesmaximal, characteristic, direct product factor, Sylow
8C23×C3×Q8C411yescharacteristic, complemented
9C24×C3×C4C2211yescharacteristic
10C22×C3×M16—21no—
11C2×C3×C22⋊Q8—21no—
12C2×C3×C22⋊Q8—21no—
13C2×C3×C22⋊Q8—21no—
14C2×C3×C22⋊Q8—21no—
15C2×C3×C22⋊Q8—21no—
16C2×C3×C22⋊Q8—21no—
17C2×C3×C22⋊Q8C412yescomplemented
18C2×C3×C22⋊Q8C412yescomplemented
19C2×C3×C22⋊Q8C412yescomplemented
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×C22⋊Q8C2212yes—
23C2×C3×#117—21no—
24C22×C3×C4⋊C4—21no—
25C22×C3×C4⋊C4C411yescharacteristic, complemented
26C22×C3×C22⋊C4—21no—
27C3×#407—21no—
28C3×#407—21no—
29C3×#407C2212yes—
30C3×#407C2212yes—
31C2×C3×C22⋊C8—21no—
32C2×C3×C22⋊C8C2212yes—
33C3×#381C2212yes—
34C3×#380—21no—
35C3×#380C2212yes—
36C3×#379—21no—
37C3×C4×C22⋊C4—21no—
38C3×C4×C22⋊C4C2212yes—
39C3×#328C22116yescomplemented
40C22×C22⋊Q8C2×C311yescharacteristic
41C2×#407C2×C311yescharacteristic
42#2280C2×C311yescharacteristic
43#1520C2×C314yescomplemented
44#1511C2×C314yescomplemented
45#1508C2×C314yescomplemented
46C25×C3D411yescharacteristic
47C22×C3×Q8—21no—
48C22×C3×Q8—21no—
49C22×C3×Q8—21no—
50C22×C3×Q8—44no—
51C22×C3×Q8C2×C412yes—
52C22×C3×Q8C2×C412yes—
53C22×C3×Q8C2×C412yes—
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4—44no—
57C23×C3×C4C2×C411yescharacteristic
58C23×C3×C4C2×C411yescharacteristic
59C23×C3×C4C2×C411yescharacteristic
60C23×C3×C4C2×C411yescharacteristic
61C23×C3×C4D411yescharacteristic
62C23×C3×C4D411yescharacteristic
63C23×C3×C4D411yescharacteristic
64C23×C3×C4D411yescharacteristic
65C23×C3×C4D411yescharacteristic
66C23×C3×C4D411yescharacteristic
67C23×C3×C4D411yescharacteristic
68C23×C3×C4C2311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C2×C3×M16—22no—
72C2×C3×M16—22no—
73C2×C3×M16—44no—
74C22×C3×C8—22no—
75C3×C22⋊Q8—22no—
76C3×C22⋊Q8—22no—
77C3×C22⋊Q8—22no—
78C3×C22⋊Q8—22no—
79C3×C22⋊Q8—22no—
80C3×C22⋊Q8—22no—
81C3×C22⋊Q8—22no—
82C3×C22⋊Q8—22no—
83C3×C22⋊Q8—22no—
84C3×C22⋊Q8—22no—
85C3×C22⋊Q8—22no—
86C3×C22⋊Q8—22no—
87C3×C22⋊Q8C2×C414yes—
88C3×C22⋊Q8C2×C414yes—
89C3×C22⋊Q8C2×C414yes—
90C3×C22⋊Q8C2314yes—
91C3×#117—44no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—22no—
101C2×C3×C4⋊C4—22no—
102C2×C3×C4⋊C4C2×C412yes—
103C2×C3×C4⋊C4C2×C412yes—
104C2×C3×C4⋊C4C2×C412yes—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—22no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C42—22no—
115C3×C22⋊C8—22no—
116C3×C22⋊C8—22no—
117C3×C22⋊C8—22no—
118C3×C22⋊C8C2314yes—
119C3×#95—22no—
120C3×#95C2314yes—
121C23×Q8C3×C411yescharacteristic, complemented
122C24×C4C22×C311yescharacteristic
123C22×M16—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8C3×C412yescomplemented
131C2×C22⋊Q8C3×C412yescomplemented
132C2×C22⋊Q8C3×C412yescomplemented
133C2×C22⋊Q8C22×C312yes—
134C2×C22⋊Q8C22×C312yes—
135C2×C22⋊Q8C22×C312yes—
136C2×#117—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4C3×C411yescharacteristic, complemented
139C22×C22⋊C4—21no—
140#407—21no—
141#407—21no—
142#407C22×C312yes—
143#407C22×C312yes—
144C2×C22⋊C8—21no—
145C2×C22⋊C8C22×C312yes—
146#381C22×C312yes—
147#380—21no—
148#380C22×C312yes—
149#379—21no—
150C4×C22⋊C4—21no—
151C4×C22⋊C4C22×C312yes—
152#328C22×C3116yescomplemented
153C24×C3—24no—
154C24×C3—42no—
155C24×C3—42no—
156C24×C3C22⋊C411yescharacteristic
157C24×C3C22⋊C411yescharacteristic
158C24×C3C22⋊C411yescharacteristic
159C24×C3C22⋊C411yescharacteristic
160C24×C3C2×D411yescharacteristic
161C24×C3C2×D411yescharacteristic
162C24×C3C2×D411yescharacteristic
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—44no—
167C2×C3×Q8—44no—
168C2×C3×Q8—44no—
169C2×C3×Q8—44no—
170C2×C3×Q8—44no—
171C2×C3×Q8—44no—
172C2×C3×Q8C22×C414yes—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4—24no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—24no—
183C22×C3×C4—42no—
184C22×C3×C4—42no—
185C22×C3×C4—42no—
186C22×C3×C4—42no—
187C22×C3×C4—42no—
188C22×C3×C4—42no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
191C22×C3×C4—42no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—44no—
195C22×C3×C4—44no—
196C22×C3×C4C22⋊C411yescharacteristic
197C22×C3×C4C22⋊C411yescharacteristic
198C22×C3×C4C22⋊C411yescharacteristic
199C22×C3×C4C22⋊C411yescharacteristic
200C22×C3×C4C22⋊C411yescharacteristic
201C22×C3×C4C22⋊C411yescharacteristic
202C22×C3×C4C22⋊C411yescharacteristic
203C22×C3×C4C22⋊C411yescharacteristic
204C22×C3×C4C22⋊C411yescharacteristic
205C22×C3×C4C22⋊C411yescharacteristic
206C22×C3×C4C22⋊C411yescharacteristic
207C22×C3×C4C22⋊C411yescharacteristic
208C22×C3×C4C22×C411yescharacteristic
209C22×C3×C4C22×C411yescharacteristic
210C22×C3×C4C22×C411yescharacteristic
211C22×C3×C4C22×C411yescharacteristic
212C22×C3×C4C22×C411yescharacteristic
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2411yescharacteristic
224C3×M16—44no—
225C3×M16—44no—
226C2×C3×C8—24no—
227C2×C3×C8—44no—
228C3×C4⋊C4—24no—
229C3×C4⋊C4—24no—
230C3×C4⋊C4—24no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—44no—
236C3×C4⋊C4C22×C414yes—
237C3×C22⋊C4—24no—
238C3×C22⋊C4—24no—
239C3×C22⋊C4—24no—
240C3×C22⋊C4—24no—
241C3×C22⋊C4—44no—
242C3×C22⋊C4—44no—
243C3×C22⋊C4—44no—
244C3×C42—44no—
245C25C3×D411yescharacteristic
246C22×Q8—21no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—44no—
250C22×Q8C2×C3×C412yes—
251C22×Q8C2×C3×C412yes—
252C22×Q8C2×C3×C412yes—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—44no—
256C23×C4C2×C3×C411yescharacteristic
257C23×C4C2×C3×C411yescharacteristic
258C23×C4C2×C3×C411yescharacteristic
259C23×C4C2×C3×C411yescharacteristic
260C23×C4C3×D411yescharacteristic
261C23×C4C3×D411yescharacteristic
262C23×C4C3×D411yescharacteristic
263C23×C4C3×D411yescharacteristic
264C23×C4C3×D411yescharacteristic
265C23×C4C3×D411yescharacteristic
266C23×C4C3×D411yescharacteristic
267C23×C4C23×C311yescharacteristic
268C23×C4C23×C311yescharacteristic
269C23×C4C23×C311yescharacteristic
270C2×M16—22no—
271C2×M16—22no—
272C2×M16—44no—
273C22×C8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—22no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8C2×C3×C414yes—
287C22⋊Q8C2×C3×C414yes—
288C22⋊Q8C2×C3×C414yes—
289C22⋊Q8C23×C314yes—
290#117—44no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4C2×C3×C412yes—
302C2×C4⋊C4C2×C3×C412yes—
303C2×C4⋊C4C2×C3×C412yes—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C42—22no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317C22⋊C8C23×C314yes—
318#95—22no—
319#95C23×C314yes—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—416no—
341C23×C3C2×C22⋊C411yescharacteristic
342C23×C3C2×C22⋊C411yescharacteristic
343C23×C3C2×C22⋊C411yescharacteristic
344C23×C3C2×C22⋊C411yescharacteristic
345C23×C3C2×C22⋊C411yescharacteristic
346C23×C3C2×C22⋊C411yescharacteristic
347C23×C3#13714yes—
348C23×C3C22×D411yescharacteristic
349C3×Q8—44no—
350C3×Q8—44no—
351C3×Q8—44no—
352C3×Q8—44no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—44no—
383C2×C3×C4—44no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—44no—
387C2×C3×C4—44no—
388C2×C3×C4—44no—
389C2×C3×C4—44no—
390C2×C3×C4—44no—
391C2×C3×C4#9914yes—
392C2×C3×C4C2×C22⋊C411yescharacteristic
393C2×C3×C4C2×C22⋊C411yescharacteristic
394C2×C3×C4C2×C22⋊C411yescharacteristic
395C2×C3×C4C2×C22⋊C411yescharacteristic
396C2×C3×C4C2×C22⋊C411yescharacteristic
397C2×C3×C4C2×C22⋊C411yescharacteristic
398C2×C3×C4C23×C411yescharacteristic
399C2×C3×C4C22×D411yescharacteristic
400C3×C8—44no—
401C24—24no—
402C24—42no—
403C24—42no—
404C24C3×C22⋊C411yescharacteristic
405C24C3×C22⋊C411yescharacteristic
406C24C3×C22⋊C411yescharacteristic
407C24C3×C22⋊C411yescharacteristic
408C24C2×C3×D411yescharacteristic
409C24C2×C3×D411yescharacteristic
410C24C2×C3×D411yescharacteristic
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8C22×C3×C414yes—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4C3×C22⋊C411yescharacteristic
445C22×C4C3×C22⋊C411yescharacteristic
446C22×C4C3×C22⋊C411yescharacteristic
447C22×C4C3×C22⋊C411yescharacteristic
448C22×C4C3×C22⋊C411yescharacteristic
449C22×C4C3×C22⋊C411yescharacteristic
450C22×C4C3×C22⋊C411yescharacteristic
451C22×C4C3×C22⋊C411yescharacteristic
452C22×C4C3×C22⋊C411yescharacteristic
453C22×C4C3×C22⋊C411yescharacteristic
454C22×C4C3×C22⋊C411yescharacteristic
455C22×C4C3×C22⋊C411yescharacteristic
456C22×C4C22×C3×C411yescharacteristic
457C22×C4C22×C3×C411yescharacteristic
458C22×C4C22×C3×C411yescharacteristic
459C22×C4C22×C3×C411yescharacteristic
460C22×C4C22×C3×C411yescharacteristic
461C22×C4C22×C3×C411yescharacteristic
462C22×C4C2×C3×D411yescharacteristic
463C22×C4C2×C3×D411yescharacteristic
464C22×C4C2×C3×D411yescharacteristic
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C2×C3×D411yescharacteristic
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C24×C311yescharacteristic
472M16—44no—
473M16—44no—
474C2×C8—24no—
475C2×C8—44no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—24no—
483C4⋊C4—44no—
484C4⋊C4C22×C3×C414yes—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—44no—
490C22⋊C4—44no—
491C22⋊C4—44no—
492C42—44no—
493C22×C3—28no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3C2×#9912yes—
517C22×C3#41912yes—
518C22×C3#41912yes—
519C22×C3#42112yes—
520C22×C3C22×C22⋊C411yescharacteristic
521C22×C3C2×#13712yes—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—44no—
529C3×C4—44no—
530C3×C4—84no—
531C3×C4C2×#9912yes—
532C3×C4C2×#9912yes—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—416no—
554C23C2×C3×C22⋊C411yescharacteristic
555C23C2×C3×C22⋊C411yescharacteristic
556C23C2×C3×C22⋊C411yescharacteristic
557C23C2×C3×C22⋊C411yescharacteristic
558C23C2×C3×C22⋊C411yescharacteristic
559C23C2×C3×C22⋊C411yescharacteristic
560C23C3×#13714yes—
561C23C22×C3×D411yescharacteristic
562Q8—44no—
563Q8—44no—
564Q8—44no—
565Q8—44no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4C3×#9914yes—
605C2×C4C2×C3×C22⋊C411yescharacteristic
606C2×C4C2×C3×C22⋊C411yescharacteristic
607C2×C4C2×C3×C22⋊C411yescharacteristic
608C2×C4C2×C3×C22⋊C411yescharacteristic
609C2×C4C2×C3×C22⋊C411yescharacteristic
610C2×C4C2×C3×C22⋊C411yescharacteristic
611C2×C4C23×C3×C411yescharacteristic
612C2×C4C22×C3×D411yescharacteristic
613C8—44no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—41no—
620C2×C3—41no—
621C2×C3C22×#9911yescharacteristic
622C2×C3C2×#41911yescharacteristic
623C2×C3C2×#42111yescharacteristic
624C22—28no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22C2×C3×#9912yes—
648C22C3×#41912yes—
649C22C3×#41912yes—
650C22C3×#42112yes—
651C22C22×C3×C22⋊C411yescharacteristic
652C22C2×C3×#13712yes—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—44no—
660C4—44no—
661C4—84no—
662C4C2×C3×#9912yes—
663C4C2×C3×#9912yes—
664C3#1757811yescharacteristic, direct product factor, Sylow
665C2—22no—
666C2—22no—
667C2—22no—
668C2—22no—
669C2—22no—
670C2—41no—
671C2—41no—
672C2C22×C3×#9911yescharacteristic
673C2C2×C3×#41911yescharacteristic
674C2C2×C3×#42111yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC25×C3D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#1520C2semidirect
5. C3×#1511C2semidirect
6. C3×#1508C2semidirect
7. #17578C3direct (N × H)
8. C23×C3×Q8C4semidirect
17. C2×C3×C22⋊Q8C4semidirect
18. C2×C3×C22⋊Q8C4semidirect
19. C2×C3×C22⋊Q8C4semidirect
25. C22×C3×C4⋊C4C4semidirect
39. C3×#328C22semidirect
43. #1520C2×C3semidirect
44. #1511C2×C3semidirect
45. #1508C2×C3semidirect
121. C23×Q8C3×C4semidirect
130. C2×C22⋊Q8C3×C4semidirect
131. C2×C22⋊Q8C3×C4semidirect
132. C2×C22⋊Q8C3×C4semidirect
138. C22×C4⋊C4C3×C4semidirect
152. #328C22×C3semidirect
664. C3#17578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#4072
C3×#22802
C3×#15202
C3×#15112
C3×#15082
#175783