Finite Group Databasebeta

← C32×#5636 #13179014

Subgroups — C32×#5636 #13179014

Order 1728.

1664 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
1C33×C22⋊Q8C211yesmaximal, characteristic, complemented
2C32×#946C211yesmaximal, characteristic, complemented
3C32×#944C211yesmaximal, characteristic, complemented
4C32×C4×#67C211yesmaximal, characteristic
5C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C32×#896C211yesmaximal, characteristic, complemented
7C32×#896C211yesmaximal, characteristic, complemented
8C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
9C32×#889C211yesmaximal, characteristic, complemented
10C32×#889C211yesmaximal, characteristic, complemented
11C32×#887C211yesmaximal, characteristic, complemented
12C32×#67⋊C4C211yesmaximal, characteristic
13C32×#67⋊C4C211yesmaximal, characteristic
14C32×#878C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#554—31nomaximal
17C3×#5636C314yesmaximal, direct product factor
18C2×C33×Q8C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic
27C2×C32×Dic6C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×#125—31no—
55C32×#125—31no—
56C32×C22⋊Q8—24no—
57C32×C22⋊Q8—31no—
58C32×C22⋊Q8—31no—
59C32×C22⋊Q8—31no—
60C32×C22⋊Q8—31no—
61C32×C22⋊Q8—31no—
62C32×C22⋊Q8D311yescharacteristic, complemented
63C32×C22⋊Q8C2×C314yescomplemented
64C32×C4×Q8—31no—
65C32×C4×D4—31no—
66C32×C4×D4—31no—
67C32×C4×D4—31no—
68C2×C32×C4⋊C4—31no—
69C2×C32×C4⋊C4—31no—
70C3×#946C2×C314yescomplemented
71C3×#944C2×C314yescomplemented
72C3×C4×#67C2×C314yes—
73C2×C3×Dic3⋊C4C2×C314yescomplemented
74C3×#896C2×C314yescomplemented
75C3×#896C2×C314yescomplemented
76C3×D3×C4⋊C4C2×C314yescomplemented
77C3×#889C2×C314yescomplemented
78C3×#889C2×C314yescomplemented
79C3×#887C2×C314yescomplemented
80C3×#67⋊C4C2×C314yes—
81C3×#67⋊C4C2×C314yes—
82C3×#878C2×C314yescomplemented
83C3×#878C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C33×Q8—41no—
87C2×C33×C4—41no—
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C32×#67Q814yescomplemented
95C2×C32×Dic3—22no—
96C2×C32×Dic3—41no—
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×C4×D3—22no—
105C32×C4×D3—41no—
106C32×C4×D3—41no—
107C32×Dic6—22no—
108C32×Dic6—41no—
109C3×#554—34no—
110#5636C3211yescharacteristic, direct product factor
111C2×C32×Q8—24no—
112C2×C32×Q8—31no—
113C2×C32×Q8—31no—
114C2×C32×Q8C2×D311yescharacteristic
115C2×C32×Q8C22×C314yes—
116C2×C32×D4—31no—
117C22×C32×C4—24no—
118C22×C32×C4—31no—
119C22×C32×C4—31no—
120C22×C32×C4—31no—
121C22×C32×C4—31no—
122C22×C32×C4—31no—
123C22×C32×C4C2×D311yescharacteristic
124C22×C32×C4C22×C314yes—
125C2×C3×#67C22×C314yes—
126C22×C3×Dic3C22×C314yes—
127C22×C3×Dic3C22×C314yes—
128C2×C3×C4×D3C22×C314yes—
129C2×C3×C4×D3C22×C314yes—
130C2×C3×C4×D3C22×C314yes—
131C2×C3×Dic6C22×C314yes—
132C2×C3×Dic6C22×C314yes—
133C32×C4⋊C4—24no—
134C32×C4⋊C4—24no—
135C32×C4⋊C4—24no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4C2×D311yescharacteristic
150C32×C4⋊C4C2×D311yescharacteristic
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C22×C314yes—
153C32×C4⋊C4C22×C314yes—
154C32×C4⋊C4C22×C314yes—
155C32×C22⋊C4—24no—
156C32×C22⋊C4—24no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4C2×D311yescharacteristic
162C32×C22⋊C4C2×D311yescharacteristic
163C32×C22⋊C4C22×C314yes—
164C32×C22⋊C4C22×C314yes—
165C32×C42—31no—
166C32×C42—31no—
167C32×C42—31no—
168C3×#217C22×C314yes—
169C3×(C2×D3)⋊C4C22×C314yes—
170C3×(C2×D3)⋊C4C22×C314yes—
171C3×(C2×D3)⋊C4C22×C314yes—
172C3×C4⋊Dic3C22×C314yes—
173C3×C4⋊Dic3C22×C314yes—
174C3×Dic3⋊C4C22×C314yes—
175C3×Dic3⋊C4C22×C314yes—
176C3×Dic3⋊C4C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×C4×Dic3C22×C314yes—
186C3×C4×Dic3C22×C314yes—
187C3×C4×Dic3C22×C314yes—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33C2×Q812yes—
191C22×C33C2411yescharacteristic
192C2×C32×D3—21no—
193C2×C32×D3—21no—
194C2×C32×D3C2×Q812yes—
195C33×C4—21no—
196C33×C4—21no—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C32×Dic3—21no—
202C32×Dic3—21no—
203C32×Dic3—21no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3C2×Q812yes—
207C32×Dic3#4112yes—
208C3×C4⋊Q8—34no—
209C3×#125—34no—
210C3×#125—34no—
211C3×C22⋊Q8—24no—
212C3×C22⋊Q8—34no—
213C3×C22⋊Q8—34no—
214C3×C22⋊Q8—34no—
215C3×C22⋊Q8—34no—
216C3×C22⋊Q8—34no—
217C3×C22⋊Q8C3×D314yescomplemented
218C3×C22⋊Q8C2×C3211yescharacteristic, complemented
219C3×C4×Q8—34no—
220C3×C4×D4—34no—
221C3×C4×D4—34no—
222C3×C4×D4—34no—
223C2×C3×C4⋊C4—34no—
224C2×C3×C4⋊C4—34no—
225#946C2×C3211yescharacteristic, complemented
226#944C2×C3211yescharacteristic, complemented
227C4×#67C2×C3211yescharacteristic
228C2×Dic3⋊C4C2×C3211yescharacteristic, complemented
229#896C2×C3211yescharacteristic, complemented
230#896C2×C3211yescharacteristic, complemented
231D3×C4⋊C4C2×C3211yescharacteristic, complemented
232#889C2×C3211yescharacteristic, complemented
233#889C2×C3211yescharacteristic, complemented
234#887C2×C3211yescharacteristic, complemented
235#67⋊C4C2×C3211yescharacteristic
236#67⋊C4C2×C3211yescharacteristic
237#878C2×C3211yescharacteristic, complemented
238#878C2×C3211yescharacteristic, complemented
239C23×C32—24no—
240C23×C32—31no—
241C23×C32C22×D311yescharacteristic
242C23×C32C23×C314yes—
243C22×C3×D3C23×C314yes—
244C32×Q8—41no—
245C32×Q8—44no—
246C32×Q8—48no—
247C32×Q8—62no—
248C32×Q8—121no—
249C32×D4—34no—
250C2×C32×C4—24no—
251C2×C32×C4—24no—
252C2×C32×C4—24no—
253C2×C32×C4—24no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—31no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—41no—
264C2×C32×C4—44no—
265C2×C32×C4—48no—
266C2×C32×C4—62no—
267C2×C32×C4—62no—
268C2×C32×C4—121no—
269C2×C32×C4—121no—
270C2×C32×C4—121no—
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C23×C314yes—
278C2×C32×C4C23×C314yes—
279C2×C32×C4C23×C314yes—
280C2×C32×C4C23×C314yes—
281C2×C32×C4C23×C314yes—
282C2×C32×C4C23×C314yes—
283C3×#67C3×Q8116yescomplemented
284C2×C3×Dic3—28no—
285C2×C3×Dic3—44no—
286C2×C3×Dic3C23×C314yes—
287C2×C3×Dic3C23×C314yes—
288C2×C3×Dic3C23×C314yes—
289C2×C3×Dic3C23×C314yes—
290C2×C3×Dic3C23×C314yes—
291C2×C3×Dic3C23×C314yes—
292C2×C3×Dic3C23×C314yes—
293C3×C4×D3—28no—
294C3×C4×D3—44no—
295C3×C4×D3—44no—
296C3×Dic6—28no—
297C3×Dic6—44no—
298#554—31noSylow
299C2×C33—22no—
300C2×C33C22×Q811yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C33H(5,𝔽2)11yescharacteristic
303C32×D3—22no—
304C2×C3×Q8—24no—
305C2×C3×Q8—34no—
306C2×C3×Q8—34no—
307C2×C3×Q8C2×C3×D314yes—
308C2×C3×Q8C22×C3211yescharacteristic
309C2×C3×D4—34no—
310C22×C3×C4—24no—
311C22×C3×C4—34no—
312C22×C3×C4—34no—
313C22×C3×C4—34no—
314C22×C3×C4—34no—
315C22×C3×C4—34no—
316C22×C3×C4C2×C3×D314yes—
317C22×C3×C4C22×C3211yescharacteristic
318C2×#67C22×C3211yescharacteristic
319C22×Dic3C22×C3211yescharacteristic
320C22×Dic3C22×C3211yescharacteristic
321C2×C4×D3C22×C3211yescharacteristic
322C2×C4×D3C22×C3211yescharacteristic
323C2×C4×D3C22×C3211yescharacteristic
324C2×Dic6C22×C3211yescharacteristic
325C2×Dic6C22×C3211yescharacteristic
326C3×C4⋊C4—24no—
327C3×C4⋊C4—24no—
328C3×C4⋊C4—24no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—34no—
334C3×C4⋊C4—34no—
335C3×C4⋊C4—34no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4—34no—
339C3×C4⋊C4—34no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—34no—
342C3×C4⋊C4C2×C3×D314yes—
343C3×C4⋊C4C2×C3×D314yes—
344C3×C4⋊C4C2×C3×D314yes—
345C3×C4⋊C4C22×C3211yescharacteristic
346C3×C4⋊C4C22×C3211yescharacteristic
347C3×C4⋊C4C22×C3211yescharacteristic
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4C2×C3×D314yes—
355C3×C22⋊C4C2×C3×D314yes—
356C3×C22⋊C4C22×C3211yescharacteristic
357C3×C22⋊C4C22×C3211yescharacteristic
358C3×C42—34no—
359C3×C42—34no—
360C3×C42—34no—
361#217C22×C3211yescharacteristic
362(C2×D3)⋊C4C22×C3211yescharacteristic
363(C2×D3)⋊C4C22×C3211yescharacteristic
364(C2×D3)⋊C4C22×C3211yescharacteristic
365C4⋊Dic3C22×C3211yescharacteristic
366C4⋊Dic3C22×C3211yescharacteristic
367Dic3⋊C4C22×C3211yescharacteristic
368Dic3⋊C4C22×C3211yescharacteristic
369Dic3⋊C4C22×C3211yescharacteristic
370Dic3⋊C4C22×C3211yescharacteristic
371Dic3⋊C4C22×C3211yescharacteristic
372Dic3⋊C4C22×C3211yescharacteristic
373Dic3⋊C4C22×C3211yescharacteristic
374Dic3⋊C4C22×C3211yescharacteristic
375Dic3⋊C4C22×C3211yescharacteristic
376Dic3⋊C4C22×C3211yescharacteristic
377Dic3⋊C4C22×C3211yescharacteristic
378C4×Dic3C22×C3211yescharacteristic
379C4×Dic3C22×C3211yescharacteristic
380C4×Dic3C22×C3211yescharacteristic
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—24no—
384C22×C32—28no—
385C22×C32—24no—
386C22×C32—24no—
387C22×C32—32no—
388C22×C32—44no—
389C22×C32—44no—
390C22×C32—61no—
391C22×C32—61no—
392C22×C32D3×Q812yes—
393C22×C32C2×C3×Q818yes—
394C22×C32C23×D311yescharacteristic
395C22×C32C24×C314yes—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3C2×C3×Q818yes—
399C32×C4—28no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—24no—
407C32×C4—24no—
408C32×C4—24no—
409C32×C4—24no—
410C32×C4—24no—
411C32×C4—24no—
412C32×C4—32no—
413C32×C4—32no—
414C32×C4—44no—
415C32×C4—44no—
416C32×C4—44no—
417C32×C4—44no—
418C32×C4—44no—
419C32×C4—61no—
420C32×C4—61no—
421C32×C4—61no—
422C32×C4—61no—
423C32×C4—61no—
424C3×Dic3—24no—
425C3×Dic3—24no—
426C3×Dic3—24no—
427C3×Dic3—24no—
428C3×Dic3—24no—
429C3×Dic3C2×C3×Q818yes—
430C3×Dic3C3×#4118yes—
431C4⋊Q8—31no—
432#125—31no—
433#125—31no—
434C22⋊Q8—31no—
435C22⋊Q8—31no—
436C22⋊Q8—31no—
437C22⋊Q8—31no—
438C22⋊Q8—31no—
439C22⋊Q8C32×D311yescharacteristic, complemented
440C4×Q8—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—31no—
446C33#55411yescharacteristic, complemented, Sylow
447C23×C3—24no—
448C23×C3—34no—
449C23×C3C22×C3×D314yes—
450C23×C3C23×C3211yescharacteristic
451C22×D3C23×C3211yescharacteristic
452C3×Q8—44no—
453C3×Q8—41no—
454C3×Q8—48no—
455C3×Q8—68no—
456C3×Q8—124no—
457C3×D4—316no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—34no—
465C2×C3×C4—34no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—44no—
472C2×C3×C4—41no—
473C2×C3×C4—48no—
474C2×C3×C4—68no—
475C2×C3×C4—68no—
476C2×C3×C4—124no—
477C2×C3×C4—124no—
478C2×C3×C4—124no—
479C2×C3×C4C22×C3×D314yes—
480C2×C3×C4C22×C3×D314yes—
481C2×C3×C4C22×C3×D314yes—
482C2×C3×C4C22×C3×D314yes—
483C2×C3×C4C22×C3×D314yes—
484C2×C3×C4C22×C3×D314yes—
485C2×C3×C4C23×C3211yescharacteristic
486C2×C3×C4C23×C3211yescharacteristic
487C2×C3×C4C23×C3211yescharacteristic
488C2×C3×C4C23×C3211yescharacteristic
489C2×C3×C4C23×C3211yescharacteristic
490C2×C3×C4C23×C3211yescharacteristic
491#67C32×Q814yescomplemented
492C2×Dic3—22no—
493C2×Dic3—41no—
494C2×Dic3C23×C3211yescharacteristic
495C2×Dic3C23×C3211yescharacteristic
496C2×Dic3C23×C3211yescharacteristic
497C2×Dic3C23×C3211yescharacteristic
498C2×Dic3C23×C3211yescharacteristic
499C2×Dic3C23×C3211yescharacteristic
500C2×Dic3C23×C3211yescharacteristic
501C4×D3—22no—
502C4×D3—41no—
503C4×D3—41no—
504Dic6—22no—
505Dic6—41no—
506C2×C32—22no—
507C2×C32—24no—
508C2×C32—24no—
509C2×C32—24no—
510C2×C32—28no—
511C2×C32—48no—
512C2×C32—62no—
513C2×C32#100411yescharacteristic
514C2×C32C2×D3×Q811yescharacteristic
515C2×C32D3×#4111yescharacteristic
516C2×C32C22×C3×Q814yes—
517C2×C32C2×C3×#4114yes—
518C2×C32C3×H(5,𝔽2)14yes—
519C3×D3—28no—
520C2×Q8—31no—
521C2×Q8—31no—
522C2×Q8C2×C32×D311yescharacteristic
523C2×D4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4C2×C32×D311yescharacteristic
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4C2×C32×D311yescharacteristic
544C4⋊C4C2×C32×D311yescharacteristic
545C4⋊C4C2×C32×D311yescharacteristic
546C22⋊C4—31no—
547C22⋊C4—31no—
548C22⋊C4—31no—
549C22⋊C4—31no—
550C22⋊C4C2×C32×D311yescharacteristic
551C22⋊C4C2×C32×D311yescharacteristic
552C42—31no—
553C42—31no—
554C42—31no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—24no—
560C22×C3—28no—
561C22×C3—38no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—64no—
565C22×C3—64no—
566C22×C3C3×D3×Q818yes—
567C22×C3C2×C32×Q812yes—
568C22×C3C23×C3×D314yes—
569C22×C3C24×C3211yescharacteristic
570C2×D3—21no—
571C2×D3—21no—
572C2×D3C2×C32×Q812yes—
573C3×C4—28no—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—24no—
577C3×C4—24no—
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—38no—
587C3×C4—38no—
588C3×C4—44no—
589C3×C4—44no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—44no—
593C3×C4—64no—
594C3×C4—64no—
595C3×C4—64no—
596C3×C4—64no—
597C3×C4—64no—
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3C2×C32×Q812yes—
604Dic3C32×#4112yes—
605C32—24no—
606C32#563611yescharacteristic, direct product factor
607C32C3×#55414yescomplemented
608C23—31no—
609C23C22×C32×D311yescharacteristic
610Q8—41no—
611Q8—62no—
612Q8—121no—
613D4—34no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—31no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—41no—
622C2×C4—62no—
623C2×C4—62no—
624C2×C4—121no—
625C2×C4—121no—
626C2×C4—121no—
627C2×C4C22×C32×D311yescharacteristic
628C2×C4C22×C32×D311yescharacteristic
629C2×C4C22×C32×D311yescharacteristic
630C2×C4C22×C32×D311yescharacteristic
631C2×C4C22×C32×D311yescharacteristic
632C2×C4C22×C32×D311yescharacteristic
633C2×C3—22no—
634C2×C3—28no—
635C2×C3—24no—
636C2×C3—24no—
637C2×C3—24no—
638C2×C3—48no—
639C2×C3—68no—
640C2×C3C3×#100414yes—
641C2×C3C2×C3×D3×Q814yes—
642C2×C3C3×D3×#4114yes—
643C2×C3C22×C32×Q811yescharacteristic
644C2×C3C2×C32×#4111yescharacteristic
645C2×C3C32×H(5,𝔽2)11yescharacteristic
646D3—22no—
647C22—21no—
648C22—21no—
649C22—32no—
650C22—61no—
651C22—61no—
652C22C32×D3×Q812yes—
653C22C23×C32×D311yescharacteristic
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—32no—
661C4—32no—
662C4—61no—
663C4—61no—
664C4—61no—
665C4—61no—
666C4—61no—
667C3—24no—
668C3C3×#563614yesdirect product factor
669C3C32×#55411yescharacteristic, complemented
670C2—22no—
671C2—62no—
672C2C32×#100411yescharacteristic
673C2C2×C32×D3×Q811yescharacteristic
674C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C22⋊Q8C2
socleC22×C33C24
prime radicalC2×C32×#67C22
hypercenterC32×C22⋊Q8D3
hypocenterC3C32×#554
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C33×C22⋊Q8C2semidirect
2. C32×#946C2semidirect
3. C32×#944C2semidirect
5. C2×C32×Dic3⋊C4C2semidirect
6. C32×#896C2semidirect
7. C32×#896C2semidirect
8. C32×D3×C4⋊C4C2semidirect
9. C32×#889C2semidirect
10. C32×#889C2semidirect
11. C32×#887C2semidirect
14. C32×#878C2semidirect
15. C32×#878C2semidirect
17. C3×#5636C3direct (N × H)
62. C32×C22⋊Q8D3semidirect
63. C32×C22⋊Q8C2×C3semidirect
70. C3×#946C2×C3semidirect
71. C3×#944C2×C3semidirect
73. C2×C3×Dic3⋊C4C2×C3semidirect
74. C3×#896C2×C3semidirect
75. C3×#896C2×C3semidirect
76. C3×D3×C4⋊C4C2×C3semidirect
77. C3×#889C2×C3semidirect
78. C3×#889C2×C3semidirect
79. C3×#887C2×C3semidirect
82. C3×#878C2×C3semidirect
83. C3×#878C2×C3semidirect
94. C32×#67Q8semidirect
110. #5636C32direct (N × H)
217. C3×C22⋊Q8C3×D3semidirect
218. C3×C22⋊Q8C2×C32semidirect
225. #946C2×C32semidirect
226. #944C2×C32semidirect
228. C2×Dic3⋊C4C2×C32semidirect
229. #896C2×C32semidirect
230. #896C2×C32semidirect
231. D3×C4⋊C4C2×C32semidirect
232. #889C2×C32semidirect
233. #889C2×C32semidirect
234. #887C2×C32semidirect
237. #878C2×C32semidirect
238. #878C2×C32semidirect
283. C3×#67C3×Q8semidirect
439. C22⋊Q8C32×D3semidirect
446. C33#554semidirect
491. #67C32×Q8semidirect
606. C32#5636direct (N × H)
607. C32C3×#554semidirect
668. C3C3×#5636direct (N × H)
669. C3C32×#554semidirect

Maximal subgroups

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

subgroupindex
C33×C22⋊Q82
C32×#9462
C32×#9442
C32×C4×#672
C2×C32×Dic3⋊C42
C32×#8962
C32×D3×C4⋊C42
C32×#8892
C32×#8872
C32×#67⋊C42
C32×#8782
C32×#5543
C3×#56363