Finite Group Databasebeta

← #10596129⋊C3 #13153048

Subgroups — #10596129⋊C3 #13153048

Order 1728.

946 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
2#64146⋊C3C211yesmaximal, characteristic
3D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4C2×#3752⋊C3C211yesmaximal, characteristic, complemented
5#64135⋊C3C211yesmaximal, characteristic, complemented
6#64107⋊C3C211yesmaximal, characteristic, complemented
7#64107⋊C3C211yesmaximal, characteristic, complemented
8#64106⋊C3C211yesmaximal, characteristic, complemented
9#64101⋊C3C211yesmaximal, characteristic, complemented
10#64095⋊C3C211yesmaximal, characteristic, complemented
11#64094⋊C3C211yesmaximal, characteristic, complemented
12#64092⋊C3C211yesmaximal, characteristic, complemented
13#64090⋊C3C211yesmaximal, characteristic, complemented
14C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
15#64087⋊C3C211yesmaximal, characteristic, complemented
16#10596129C311yesmaximal, characteristic, complemented
17C3×#5658—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×D4×H(3,𝔽3)C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×#634⋊C3C2211yescharacteristic, complemented
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
32C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic, complemented
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
47C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
48#3750⋊C3C2211yescharacteristic, complemented
49#3750⋊C3C2211yescharacteristic, complemented
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
53C32×#123—21no—
54C32×#123D311yescharacteristic, complemented
55C32×#123C2×C311yescharacteristic, complemented
56#64146C2×C311yescharacteristic
57D4×C3⋊Dic3C2×C311yescharacteristic, complemented
58C2×#3752C2×C311yescharacteristic, complemented
59#64135C2×C311yescharacteristic, complemented
60#64107C2×C311yescharacteristic, complemented
61#64107C2×C311yescharacteristic, complemented
62#64106C2×C311yescharacteristic, complemented
63#64101C2×C311yescharacteristic, complemented
64#64095C2×C311yescharacteristic, complemented
65#64094C2×C311yescharacteristic, complemented
66#64092C2×C311yescharacteristic, complemented
67#64090C2×C311yescharacteristic, complemented
68C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
69#64087C2×C311yescharacteristic, complemented
70C3×#937—31no—
71C3×D4×Dic3—31no—
72C2×C3×(C2×D3)⋊C4—31no—
73C3×#926—31no—
74C3×#898—31no—
75C3×#898—31no—
76C3×#897—31no—
77C3×#892—31no—
78C3×#886—31no—
79C3×#885—31no—
80C3×#883—31no—
81C3×#67⋊C4—31no—
82C3×D3×C22⋊C4—31no—
83C3×#878—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—22no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91D4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)—22no—
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97C2×C4×H(3,𝔽3)C2311yescharacteristic
98#638⋊C3—22no—
99#638⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3—41no—
101C2×(C3⋊Dic3)⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C4×(C3⋊D3)⋊C3—22no—
109C4×(C3⋊D3)⋊C3—41no—
110#634⋊C3—41no—
111C3×#551—91no—
112#5658—31no—
113#5658—91no—
114C23×C3⋊D3C22×C311yescharacteristic
115C23×C3×D3—31no—
116C2×C32×D4—21no—
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C22×C311yescharacteristic
119C22×C32×C4—21no—
120C22×C32×C4C2×D311yescharacteristic
121C22×C32×C4C22×C311yescharacteristic
122C2×#638C22×C311yescharacteristic
123C2×#638C22×C311yescharacteristic
124C22×C3⋊Dic3C22×C311yescharacteristic
125C22×C3⋊Dic3C22×C311yescharacteristic, complemented
126C2×C4×C3⋊D3C22×C311yescharacteristic
127C2×C4×C3⋊D3C22×C311yescharacteristic
128C2×#634C22×C311yescharacteristic, complemented
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C22×C3×Dic3—31no—
132C22×C3×Dic3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×Dic6—31no—
136C32×C4⋊C4—21no—
137C32×C4⋊C4—21no—
138C32×C4⋊C4C2×D311yescharacteristic, complemented
139C32×C4⋊C4C2×D311yescharacteristic, complemented
140C32×C4⋊C4C22×C311yescharacteristic, complemented
141C32×C4⋊C4C22×C311yescharacteristic, complemented
142C32×C22⋊C4—21no—
143C32×C22⋊C4—21no—
144C32×C22⋊C4—21no—
145C32×C22⋊C4C2×D311yescharacteristic
146C32×C22⋊C4C2×D311yescharacteristic, complemented
147C32×C22⋊C4C2×D311yescharacteristic, complemented
148C32×C22⋊C4C22×C311yescharacteristic
149C32×C22⋊C4C22×C311yescharacteristic, complemented
150C32×C22⋊C4C22×C311yescharacteristic, complemented
151#3757C22×C311yescharacteristic
152#3757C22×C311yescharacteristic
153#3757C22×C311yescharacteristic, complemented
154#3752C22×C311yescharacteristic
155#3752C22×C311yescharacteristic
156#3752C22×C311yescharacteristic
157#3752C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160#3752C22×C311yescharacteristic
161#3752C22×C311yescharacteristic
162C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
163C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
164C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
165C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
166#3750C22×C311yescharacteristic, complemented
167#3750C22×C311yescharacteristic, complemented
168C4×C3⋊Dic3C22×C311yescharacteristic, complemented
169C4×C3⋊Dic3C22×C311yescharacteristic, complemented
170C4×C3⋊Dic3C22×C311yescharacteristic, complemented
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×C4×Dic3—31no—
189C3×C4×Dic3—31no—
190C3×C4×Dic3—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)#4112yes—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—44no—
204C2×(C3⋊D3)⋊C3#4112yes—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207C4×H(3,𝔽3)—21no—
208C4×H(3,𝔽3)—21no—
209C4×H(3,𝔽3)—21no—
210(C3⋊Dic3)⋊C3—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#126—91no—
217C3×#126—91no—
218C3×#124—91no—
219C3×#123—31no—
220C3×#123—31no—
221C3×#123—61no—
222C3×#123—91no—
223C3×#123—91no—
224C3×#123C3×D311yescharacteristic
225C3×C22⋊Q8—91no—
226C3×C22⋊Q8—91no—
227C3×#120—91no—
228C3×C4×D4—91no—
229C3×C4×D4—91no—
230C3×#117—91no—
231C3×#117—91no—
232C2×C3×C22⋊C4—91no—
233C2×C3×C22⋊C4—91no—
234#937—31no—
235#937—91no—
236D4×Dic3—31no—
237D4×Dic3—91no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—91no—
240#926—31no—
241#926—91no—
242#898—31no—
243#898—31no—
244#898—91no—
245#898—91no—
246#897—31no—
247#897—91no—
248#892—31no—
249#892—91no—
250#886—31no—
251#886—91no—
252#885—31no—
253#885—91no—
254#883—31no—
255#883—91no—
256#67⋊C4—31no—
257#67⋊C4—91no—
258D3×C22⋊C4—31no—
259D3×C22⋊C4—91no—
260#878—31no—
261#878—91no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C23×C32C23×C311yescharacteristic
267C23×C32C23×C311yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—41no—
271C22×C3⋊D3C23×C311yescharacteristic
272C22×C3⋊D3C23×C311yescharacteristic
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—121no—
278C32×D4—22no—
279C32×D4—22no—
280C32×D4—42no—
281C2×C32×C4—22no—
282C2×C32×C4—22no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—42no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295C2×C32×C4C23×C311yescharacteristic
296C2×C32×C4C23×C311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298C2×C32×C4C23×C311yescharacteristic
299#638—22no—
300#638—41no—
301C2×C3⋊Dic3—41no—
302C2×C3⋊Dic3—41no—
303C2×C3⋊Dic3C23×C311yescharacteristic
304C2×C3⋊Dic3C23×C311yescharacteristic
305C2×C3⋊Dic3C23×C311yescharacteristic
306C2×C3⋊Dic3C23×C311yescharacteristic
307C2×C3⋊Dic3C23×C311yescharacteristic
308C2×C3⋊Dic3C23×C311yescharacteristic
309C4×C3⋊D3—22no—
310C4×C3⋊D3—41no—
311#634—41no—
312C3×#67—62no—
313C3×#67—121no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—121no—
321C2×C3×Dic3—121no—
322C3×C4×D3—62no—
323C3×C4×D3—121no—
324C3×Dic6—121no—
325#551—91noSylow
326C2×H(3,𝔽3)—22no—
327C2×H(3,𝔽3)—41no—
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)C2×#4111yescharacteristic
330C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
331(C3⋊D3)⋊C3—22no—
332(C3⋊D3)⋊C3—41no—
333C24×C3—91no—
334C23×D3—31no—
335C23×D3—91no—
336C2×C3×Q8—91no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C2×C3×D4—91no—
341C2×C3×D4—91no—
342C2×C3×D4C2×C3×D311yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—91no—
347C22×C3×C4—91no—
348C22×C3×C4—91no—
349C22×C3×C4—91no—
350C22×C3×C4C2×C3×D311yescharacteristic
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—91no—
354C2×#67—91no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×Dic6—31no—
364C2×Dic6—91no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4C2×C3×D311yescharacteristic
378C3×C4⋊C4C2×C3×D311yescharacteristic
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—31no—
382C3×C22⋊C4—31no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4—91no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4C2×C3×D311yescharacteristic
400C3×C22⋊C4C2×C3×D311yescharacteristic
401C3×C22⋊C4C2×C3×D311yescharacteristic
402C3×C42—91no—
403C3×C42—91no—
404C3×C42—91no—
405#217—31no—
406#217—31no—
407#217—31no—
408#217—91no—
409#217—91no—
410#217—91no—
411(C2×D3)⋊C4—31no—
412(C2×D3)⋊C4—31no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—31no—
430C4⋊Dic3—31no—
431C4⋊Dic3—91no—
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—91no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—31no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—22no—
457C22×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32#23712yes—
463C22×C32C3×#4112yes—
464C22×C32C23×D311yescharacteristic
465C22×C32C24×C311yescharacteristic
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—44no—
472C2×C3⋊D3C3×#4112yes—
473C2×C3×D3—32no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—124no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—41no—
491C32×C4—41no—
492C32×C4—41no—
493C32×C4—41no—
494C32×C4—41no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—61no—
507#126—91no—
508#126—91no—
509#124—91no—
510#123—91no—
511#123—91no—
512#123(C3⋊D3)⋊C311yescharacteristic, complemented
513C22⋊Q8—91no—
514C22⋊Q8—91no—
515#120—91no—
516C4×D4—91no—
517C4×D4—91no—
518#117—91no—
519#117—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
523C23×C3—31no—
524C23×C3—31no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—91no—
530C23×C3—91no—
531C23×C3—182no—
532C23×C3—182no—
533C23×C3—361no—
534C23×C3C22×C3×D311yescharacteristic
535C23×C3C22×C3×D311yescharacteristic
536C22×D3—31no—
537C22×D3—31no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—91no—
541C22×D3—91no—
542C22×D3—121no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—361no—
546C3×Q8—361no—
547C3×D4—22no—
548C3×D4—62no—
549C3×D4—62no—
550C3×D4—122no—
551C3×D4—182no—
552C3×D4—361no—
553C2×C3×C4—22no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—122no—
578C2×C3×C4—182no—
579C2×C3×C4—361no—
580C2×C3×C4—361no—
581C2×C3×C4—361no—
582C2×C3×C4C22×C3×D311yescharacteristic
583C2×C3×C4C22×C3×D311yescharacteristic
584C2×C3×C4C22×C3×D311yescharacteristic
585C2×C3×C4C22×C3×D311yescharacteristic
586C2×C3×C4C22×C3×D311yescharacteristic
587#67—62no—
588#67—121no—
589#67—182no—
590#67—361no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—361no—
606C2×Dic3—361no—
607C4×D3—62no—
608C4×D3—121no—
609C4×D3—182no—
610C4×D3—361no—
611Dic6—121no—
612Dic6—361no—
613C2×C32—22no—
614C2×C32—22no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—42no—
619C2×C32—41no—
620C2×C32—41no—
621C2×C32—81no—
622C2×C32C2×#23711yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32#100911yescharacteristic
625C2×C32C2×C3×#4111yescharacteristic
626C2×C32C2×C3×#4111yescharacteristic
627C2×C32C3×H(5,𝔽2)11yescharacteristic
628C3⋊D3—22no—
629C3⋊D3—41no—
630C3×D3—62no—
631C3×D3—121no—
632C24—91no—
633C2×Q8—91no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—91no—
641C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—91no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
649C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
662C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
663C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
664C42—91no—
665C42—91no—
666C42—91no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—31no—
673C22×C3—31no—
674C22×C3—32no—
675C22×C3—32no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—62no—
688C22×C3—92no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—364no—
700C22×C3C3×#23712yes—
701C22×C3C23×C3×D311yescharacteristic
702C2×D3—32no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—92no—
709C2×D3—124no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—61no—
729C3×C4—61no—
730C3×C4—61no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4—121no—
736C3×C4—181no—
737C3×C4—181no—
738C3×C4—181no—
739C3×C4—181no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—61no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754C32—21no—
755C32#565811yescharacteristic, complemented
756C32C3×#55111yescharacteristic, complemented
757C23—91no—
758C23—91no—
759C23—182no—
760C23—182no—
761C23—361no—
762C23C22×(C3⋊D3)⋊C311yescharacteristic
763C23C22×(C3⋊D3)⋊C311yescharacteristic
764Q8—361no—
765D4—22no—
766D4—182no—
767D4—361no—
768C2×C4—22no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—182no—
776C2×C4—361no—
777C2×C4—361no—
778C2×C4—361no—
779C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
780C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
781C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
782C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
783C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
784C2×C3—22no—
785C2×C3—31no—
786C2×C3—31no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—31no—
791C2×C3—41no—
792C2×C3—62no—
793C2×C3—62no—
794C2×C3—61no—
795C2×C3—61no—
796C2×C3—61no—
797C2×C3—122no—
798C2×C3—121no—
799C2×C3—121no—
800C2×C3—182no—
801C2×C3—241no—
802C2×C3—361no—
803C2×C3C2×C3×#23711yescharacteristic
804C2×C3C3×D3×#4111yescharacteristic
805C2×C3C3×#100911yescharacteristic
806D3—62no—
807D3—121no—
808D3—182no—
809D3—361no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—92no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—364no—
822C22#3830⋊C312yes—
823C22C23×(C3⋊D3)⋊C311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—181no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C3—31no—
836C3—31no—
837C3—61no—
838C3C3×#565811yescharacteristic
839C2—22no—
840C2—41no—
841C2—182no—
842C2—361no—
843C2C2×#3830⋊C311yescharacteristic
844C2#41×(C3⋊D3)⋊C311yescharacteristic
845C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
prime radical#64146⋊C3C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#123C2semidirect
3. D4×(C3⋊Dic3)⋊C3C2semidirect
4. C2×#3752⋊C3C2semidirect
5. #64135⋊C3C2semidirect
6. #64107⋊C3C2semidirect
7. #64107⋊C3C2semidirect
8. #64106⋊C3C2semidirect
9. #64101⋊C3C2semidirect
10. #64095⋊C3C2semidirect
11. #64094⋊C3C2semidirect
12. #64092⋊C3C2semidirect
13. #64090⋊C3C2semidirect
14. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
15. #64087⋊C3C2semidirect
16. #10596129C3semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×#634⋊C3C22semidirect
28. C4⋊C4×H(3,𝔽3)C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
31. C22⋊C4×H(3,𝔽3)C22semidirect
32. C22⋊C4×H(3,𝔽3)C22semidirect
35. #3757⋊C3C22semidirect
44. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
47. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
48. #3750⋊C3C22semidirect
49. #3750⋊C3C22semidirect
50. C4×(C3⋊Dic3)⋊C3C22semidirect
51. C4×(C3⋊Dic3)⋊C3C22semidirect
52. C4×(C3⋊Dic3)⋊C3C22semidirect
54. C32×#123D3semidirect
55. C32×#123C2×C3semidirect
57. D4×C3⋊Dic3C2×C3semidirect
58. C2×#3752C2×C3semidirect
59. #64135C2×C3semidirect
60. #64107C2×C3semidirect
61. #64107C2×C3semidirect
62. #64106C2×C3semidirect
63. #64101C2×C3semidirect
64. #64095C2×C3semidirect
65. #64094C2×C3semidirect
66. #64092C2×C3semidirect
67. #64090C2×C3semidirect
68. C22⋊C4×C3⋊D3C2×C3semidirect
69. #64087C2×C3semidirect
125. C22×C3⋊Dic3C22×C3semidirect
128. C2×#634C22×C3semidirect
138. C32×C4⋊C4C2×D3semidirect
139. C32×C4⋊C4C2×D3semidirect
140. C32×C4⋊C4C22×C3semidirect
141. C32×C4⋊C4C22×C3semidirect
146. C32×C22⋊C4C2×D3semidirect
147. C32×C22⋊C4C2×D3semidirect
149. C32×C22⋊C4C22×C3semidirect
150. C32×C22⋊C4C22×C3semidirect
153. #3757C22×C3semidirect
162. C4⋊(C3⋊Dic3)C22×C3semidirect
163. C4⋊(C3⋊Dic3)C22×C3semidirect
164. C4⋊(C3⋊Dic3)C22×C3semidirect
165. C4⋊(C3⋊Dic3)C22×C3semidirect
166. #3750C22×C3semidirect
167. #3750C22×C3semidirect
168. C4×C3⋊Dic3C22×C3semidirect
169. C4×C3⋊Dic3C22×C3semidirect
170. C4×C3⋊Dic3C22×C3semidirect
512. #123(C3⋊D3)⋊C3semidirect
522. H(3,𝔽3)#551semidirect
648. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
649. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
662. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
663. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
755. C32#5658semidirect
756. C32C3×#551semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1232
#64146⋊C32
D4×(C3⋊Dic3)⋊C32
C2×#3752⋊C32
#64135⋊C32
#64107⋊C32
#64106⋊C32
#64101⋊C32
#64095⋊C32
#64094⋊C32
#64092⋊C32
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#105961293
C3×#56583