Finite Group Databasebeta

← #10595998⋊C3 #13152521

Subgroups — #10595998⋊C3 #13152521

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#117C211yesmaximal, characteristic, complemented
2#64138⋊C3C211yesmaximal, characteristic, complemented
3C2×#3752⋊C3C211yesmaximal, characteristic, complemented
4#64107⋊C3C211yesmaximal, characteristic, complemented
5#64105⋊C3C211yesmaximal, characteristic, complemented
6#64103⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C211yesmaximal, characteristic, complemented
8#64091⋊C3C211yesmaximal, characteristic
9#64090⋊C3C211yesmaximal, characteristic, complemented
10C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
11#64087⋊C3C211yesmaximal, characteristic, complemented
12#11721387C211yesmaximal, characteristic, complemented
13#64084⋊C3C211yesmaximal, characteristic, complemented
14C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
15#64081⋊C3C211yesmaximal, characteristic, complemented
16#10595998C311yesmaximal, characteristic, complemented
17C3×#5527—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
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
32C42×H(3,𝔽3)C2211yescharacteristic, complemented
33C42×H(3,𝔽3)C2211yescharacteristic, complemented
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48#3750⋊C3C2211yescharacteristic, complemented
49#3750⋊C3C2211yescharacteristic, complemented
50#3750⋊C3C2211yescharacteristic, complemented
51#3750⋊C3C2211yescharacteristic, complemented
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
53C32×#117—21no—
54C32×#117D311yescharacteristic, complemented
55C32×#117C2×C311yescharacteristic, complemented
56#64138C2×C311yescharacteristic, complemented
57C2×#3752C2×C311yescharacteristic, complemented
58#64107C2×C311yescharacteristic, complemented
59#64105C2×C311yescharacteristic, complemented
60#64103C2×C311yescharacteristic, complemented
61#64103C2×C311yescharacteristic, complemented
62#64091C2×C311yescharacteristic
63#64090C2×C311yescharacteristic, complemented
64C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
65#64087C2×C311yescharacteristic, complemented
66#64085C2×C311yescharacteristic, complemented
67#64084C2×C311yescharacteristic, complemented
68C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
69#64081C2×C311yescharacteristic, complemented
70C3×#929—31no—
71C2×C3×(C2×D3)⋊C4—31no—
72C3×#898—31no—
73C3×#896—31no—
74C3×#894—31no—
75C3×#894—31no—
76C3×#882—31no—
77C3×#67⋊C4—31no—
78C3×D3×C22⋊C4—31no—
79C3×#878—31no—
80C3×#876—31no—
81C3×#875—31no—
82C3×C4×D12—31no—
83C3×#872—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3—22no—
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
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—
99C2×(C3⋊Dic3)⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C4⋊((C3⋊D3)⋊C3)—22no—
106C4⋊((C3⋊D3)⋊C3)—41no—
107C4×(C3⋊D3)⋊C3—22no—
108C4×(C3⋊D3)⋊C3—41no—
109C4×(C3⋊D3)⋊C3—41no—
110#634⋊C3—41no—
111C3×#551—91no—
112#5527—31no—
113#5527—91no—
114C23×C3⋊D3C22×C311yescharacteristic
115C23×C3×D3—31no—
116C22×C32×C4—21no—
117C22×C32×C4C2×D311yescharacteristic
118C22×C32×C4C22×C311yescharacteristic
119C2×#638C22×C311yescharacteristic
120C22×C3⋊Dic3C22×C311yescharacteristic
121C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
122C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
123C2×C4×C3⋊D3C22×C311yescharacteristic
124C2×C4×C3⋊D3C22×C311yescharacteristic
125C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
126C2×#634C22×C311yescharacteristic, complemented
127C2×C3×#67—31no—
128C22×C3×Dic3—31no—
129C2×C3×D12—31no—
130C2×C3×D12—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×Dic6—31no—
135C32×C4⋊C4—21no—
136C32×C4⋊C4—21no—
137C32×C4⋊C4C2×D311yescharacteristic, complemented
138C32×C4⋊C4C2×D311yescharacteristic, complemented
139C32×C4⋊C4C22×C311yescharacteristic, complemented
140C32×C4⋊C4C22×C311yescharacteristic, complemented
141C32×C22⋊C4—21no—
142C32×C22⋊C4—21no—
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C22⋊C4C2×D311yescharacteristic
145C32×C22⋊C4C22×C311yescharacteristic
146C32×C22⋊C4C22×C311yescharacteristic
147C32×C42—21no—
148C32×C42—21no—
149C32×C42C2×D311yescharacteristic, complemented
150C32×C42C2×D311yescharacteristic, complemented
151C32×C42C22×C311yescharacteristic, complemented
152C32×C42C22×C311yescharacteristic, complemented
153#3757C22×C311yescharacteristic
154#3752C22×C311yescharacteristic
155#3752C22×C311yescharacteristic
156#3752C22×C311yescharacteristic
157#3752C22×C311yescharacteristic
158#3752C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160#3752C22×C311yescharacteristic
161#3752C22×C311yescharacteristic
162#3752C22×C311yescharacteristic, complemented
163#3752C22×C311yescharacteristic, complemented
164#3752C22×C311yescharacteristic, complemented
165C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
166#3750C22×C311yescharacteristic, complemented
167#3750C22×C311yescharacteristic, complemented
168#3750C22×C311yescharacteristic, complemented
169#3750C22×C311yescharacteristic, complemented
170#3750C22×C311yescharacteristic, complemented
171C4×C3⋊Dic3C22×C311yescharacteristic, complemented
172C3×#217—31no—
173C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×C4⋊Dic3—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×C4×Dic3—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)#4112yes—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
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—
210C4×H(3,𝔽3)—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—91no—
220C3×#123—91no—
221C3×#123—91no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8—91no—
224C3×#120—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C3×#117—31no—
228C3×#117—31no—
229C3×#117—61no—
230C3×#117—91no—
231C3×#117C3×D311yescharacteristic
232C2×C3×C22⋊C4—91no—
233C2×C3×C22⋊C4—91no—
234#929—31no—
235#929—91no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—91no—
238#898—31no—
239#898—91no—
240#896—31no—
241#896—91no—
242#894—31no—
243#894—31no—
244#894—91no—
245#894—91no—
246#882—31no—
247#882—91no—
248#67⋊C4—31no—
249#67⋊C4—91no—
250D3×C22⋊C4—31no—
251D3×C22⋊C4—91no—
252#878—31no—
253#878—91no—
254#876—31no—
255#876—91no—
256#875—31no—
257#875—91no—
258C4×D12—31no—
259C4×D12—91no—
260#872—31no—
261#872—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C23×C311yescharacteristic
265C22×C3⋊D3—22no—
266C22×C3⋊D3—22no—
267C22×C3⋊D3—41no—
268C22×C3⋊D3C23×C311yescharacteristic
269C22×C3⋊D3C23×C311yescharacteristic
270C22×C3⋊D3C23×C311yescharacteristic
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—121no—
277C2×C32×C4—24no—
278C2×C32×C4—22no—
279C2×C32×C4—22no—
280C2×C32×C4—21no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C23×C311yescharacteristic
293C2×C32×C4C23×C311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295C2×C32×C4C23×C311yescharacteristic
296C2×C32×C4C23×C311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298#638—22no—
299C2×C3⋊Dic3—41no—
300C2×C3⋊Dic3C23×C311yescharacteristic
301C2×C3⋊Dic3C23×C311yescharacteristic
302C2×C3⋊Dic3C23×C311yescharacteristic
303C2×C3⋊Dic3C23×C311yescharacteristic
304C2×C3⋊Dic3C23×C311yescharacteristic
305C4⋊(C3⋊D3)—22no—
306C4⋊(C3⋊D3)—41no—
307C4×C3⋊D3—22no—
308C4×C3⋊D3—41no—
309C4×C3⋊D3—41no—
310#634—41no—
311C3×#67—62no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—121no—
318C3×D12—62no—
319C3×D12—121no—
320C3×C4×D3—62no—
321C3×C4×D3—121no—
322C3×C4×D3—121no—
323C3×Dic6—121no—
324#551—91noSylow
325C2×H(3,𝔽3)—22no—
326C2×H(3,𝔽3)C2×#4111yescharacteristic
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
329(C3⋊D3)⋊C3—22no—
330(C3⋊D3)⋊C3—41no—
331(C3⋊D3)⋊C3—41no—
332C24×C3—91no—
333C23×D3—31no—
334C23×D3—91no—
335C2×C3×Q8—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4—91no—
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C22×C3×C4C2×C3×D311yescharacteristic
347C2×#67—31no—
348C2×#67—91no—
349C22×Dic3—31no—
350C22×Dic3—91no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—91no—
354C2×D12—91no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×Dic6—31no—
362C2×Dic6—91no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C4⋊C4—91no—
375C3×C4⋊C4C2×C3×D311yescharacteristic
376C3×C4⋊C4C2×C3×D311yescharacteristic
377C3×C22⋊C4—31no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4—91no—
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⋊C4C2×C3×D311yescharacteristic
396C3×C22⋊C4C2×C3×D311yescharacteristic
397C3×C42—31no—
398C3×C42—31no—
399C3×C42—31no—
400C3×C42—31no—
401C3×C42—61no—
402C3×C42—61no—
403C3×C42—91no—
404C3×C42C2×C3×D311yescharacteristic
405C3×C42C2×C3×D311yescharacteristic
406#217—31no—
407#217—91no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
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—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430C4⋊Dic3—31no—
431C4⋊Dic3—91no—
432Dic3⋊C4—31no—
433Dic3⋊C4—31no—
434Dic3⋊C4—31no—
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—31no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—22no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32#23512yes—
453C22×C32C3×#4112yes—
454C22×C32C23×D311yescharacteristic
455C22×C32C24×C311yescharacteristic
456C2×C3⋊D3—21no—
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—44no—
465C2×C3⋊D3C3×#4112yes—
466C2×C3×D3—32no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—124no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—21no—
479C32×C4—21no—
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—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504#126—91no—
505#126—91no—
506#124—91no—
507#123—91no—
508#123—91no—
509#123—91no—
510C22⋊Q8—91no—
511C22⋊Q8—91no—
512#120—91no—
513C4×D4—91no—
514C4×D4—91no—
515#117—91no—
516#117(C3⋊D3)⋊C311yescharacteristic, complemented
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
520C23×C3—31no—
521C23×C3—31no—
522C23×C3—61no—
523C23×C3—91no—
524C23×C3—91no—
525C23×C3—91no—
526C23×C3—182no—
527C23×C3—182no—
528C23×C3—361no—
529C23×C3C22×C3×D311yescharacteristic
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—31no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—91no—
536C22×D3—91no—
537C22×D3—91no—
538C22×D3—121no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—361no—
542C3×Q8—361no—
543C3×D4—182no—
544C3×D4—182no—
545C3×D4—361no—
546C2×C3×C4—22no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—64no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4—361no—
575C2×C3×C4—361no—
576C2×C3×C4—361no—
577C2×C3×C4C22×C3×D311yescharacteristic
578C2×C3×C4C22×C3×D311yescharacteristic
579C2×C3×C4C22×C3×D311yescharacteristic
580C2×C3×C4C22×C3×D311yescharacteristic
581C2×C3×C4C22×C3×D311yescharacteristic
582C2×C3×C4C22×C3×D311yescharacteristic
583#67—62no—
584#67—182no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—121no—
596C2×Dic3—361no—
597D12—62no—
598D12—121no—
599D12—182no—
600D12—361no—
601C4×D3—62no—
602C4×D3—121no—
603C4×D3—121no—
604C4×D3—182no—
605C4×D3—361no—
606C4×D3—361no—
607Dic6—121no—
608Dic6—361no—
609C2×C32—22no—
610C2×C32—22no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—42no—
615C2×C32C2×#23511yescharacteristic
616C2×C32D3×#4111yescharacteristic
617C2×C32#100911yescharacteristic
618C2×C32C2×C3×#4111yescharacteristic
619C2×C32C2×C3×#4111yescharacteristic
620C2×C32C3×H(5,𝔽2)11yescharacteristic
621C3⋊D3—22no—
622C3⋊D3—41no—
623C3⋊D3—41no—
624C3×D3—62no—
625C3×D3—121no—
626C3×D3—121no—
627C24—91no—
628C2×Q8—91no—
629C2×D4—91no—
630C2×D4—91no—
631C2×D4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
644C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
658C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
659C42—91no—
660C42C2×(C3⋊D3)⋊C311yescharacteristic, complemented
661C42C2×(C3⋊D3)⋊C311yescharacteristic, complemented
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—31no—
665C22×C3—31no—
666C22×C3—32no—
667C22×C3—32no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—62no—
674C22×C3—92no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—181no—
682C22×C3—181no—
683C22×C3—181no—
684C22×C3—181no—
685C22×C3—364no—
686C22×C3C3×#23512yes—
687C22×C3C23×C3×D311yescharacteristic
688C2×D3—32no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—92no—
698C2×D3—124no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—181no—
706C2×D3—181no—
707C2×D3—364no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—181no—
733C3×C4—181no—
734C3×C4—181no—
735C3×C4—181no—
736C3×C4—181no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—181no—
743Dic3—181no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747C32—21no—
748C32#552711yescharacteristic, complemented
749C32C3×#55111yescharacteristic, complemented
750C23—91no—
751C23—91no—
752C23—91no—
753C23—182no—
754C23—182no—
755C23—361no—
756C23C22×(C3⋊D3)⋊C311yescharacteristic
757Q8—361no—
758D4—182no—
759D4—182no—
760D4—361no—
761C2×C4—22no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—182no—
768C2×C4—361no—
769C2×C4—361no—
770C2×C4—361no—
771C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
772C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
773C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
774C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
775C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
776C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
777C2×C3—22no—
778C2×C3—31no—
779C2×C3—31no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—31no—
784C2×C3—62no—
785C2×C3—62no—
786C2×C3—61no—
787C2×C3—61no—
788C2×C3—61no—
789C2×C3—122no—
790C2×C3—182no—
791C2×C3—361no—
792C2×C3—361no—
793C2×C3C2×C3×#23511yescharacteristic
794C2×C3C3×D3×#4111yescharacteristic
795C2×C3C3×#100911yescharacteristic
796D3—62no—
797D3—121no—
798D3—121no—
799D3—182no—
800D3—361no—
801D3—361no—
802C22—21no—
803C22—21no—
804C22—92no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—364no—
814C22#3828⋊C312yes—
815C22C23×(C3⋊D3)⋊C311yescharacteristic
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—21no—
822C4—181no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—181no—
827C3—31no—
828C3—31no—
829C3—61no—
830C3C3×#552711yescharacteristic
831C2—22no—
832C2—182no—
833C2—361no—
834C2—361no—
835C2C2×#3828⋊C311yescharacteristic
836C2#41×(C3⋊D3)⋊C311yescharacteristic
837C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#117C2
prime radical#64091⋊C3C2
hypercenter#117(C3⋊D3)⋊C3
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#117C2semidirect
2. #64138⋊C3C2semidirect
3. C2×#3752⋊C3C2semidirect
4. #64107⋊C3C2semidirect
5. #64105⋊C3C2semidirect
6. #64103⋊C3C2semidirect
7. #64103⋊C3C2semidirect
9. #64090⋊C3C2semidirect
10. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
11. #64087⋊C3C2semidirect
12. #11721387C2semidirect
13. #64084⋊C3C2semidirect
14. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
15. #64081⋊C3C2semidirect
16. #10595998C3semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
27. C2×#634⋊C3C22semidirect
28. C4⋊C4×H(3,𝔽3)C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
32. C42×H(3,𝔽3)C22semidirect
33. C42×H(3,𝔽3)C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
47. #3750⋊C3C22semidirect
48. #3750⋊C3C22semidirect
49. #3750⋊C3C22semidirect
50. #3750⋊C3C22semidirect
51. #3750⋊C3C22semidirect
52. C4×(C3⋊Dic3)⋊C3C22semidirect
54. C32×#117D3semidirect
55. C32×#117C2×C3semidirect
56. #64138C2×C3semidirect
57. C2×#3752C2×C3semidirect
58. #64107C2×C3semidirect
59. #64105C2×C3semidirect
60. #64103C2×C3semidirect
61. #64103C2×C3semidirect
63. #64090C2×C3semidirect
64. C22⋊C4×C3⋊D3C2×C3semidirect
65. #64087C2×C3semidirect
66. #64085C2×C3semidirect
67. #64084C2×C3semidirect
68. C4×C4⋊(C3⋊D3)C2×C3semidirect
69. #64081C2×C3semidirect
125. C2×C4×C3⋊D3C22×C3semidirect
126. C2×#634C22×C3semidirect
137. C32×C4⋊C4C2×D3semidirect
138. C32×C4⋊C4C2×D3semidirect
139. C32×C4⋊C4C22×C3semidirect
140. C32×C4⋊C4C22×C3semidirect
149. C32×C42C2×D3semidirect
150. C32×C42C2×D3semidirect
151. C32×C42C22×C3semidirect
152. C32×C42C22×C3semidirect
162. #3752C22×C3semidirect
163. #3752C22×C3semidirect
164. #3752C22×C3semidirect
165. C4⋊(C3⋊Dic3)C22×C3semidirect
166. #3750C22×C3semidirect
167. #3750C22×C3semidirect
168. #3750C22×C3semidirect
169. #3750C22×C3semidirect
170. #3750C22×C3semidirect
171. C4×C3⋊Dic3C22×C3semidirect
516. #117(C3⋊D3)⋊C3semidirect
519. H(3,𝔽3)#551semidirect
643. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
644. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
660. C42C2×(C3⋊D3)⋊C3semidirect
661. C42C2×(C3⋊D3)⋊C3semidirect
748. C32#5527semidirect
749. 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)×#1172
#64138⋊C32
C2×#3752⋊C32
#64107⋊C32
#64105⋊C32
#64103⋊C32
#64091⋊C32
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#117213872
#64084⋊C32
C4×C4⋊((C3⋊D3)⋊C3)2
#64081⋊C32
#105959983
C3×#55273