Finite Group Databasebeta

← #10596180⋊C3 #13153240

Subgroups — #10596180⋊C3 #13153240

Order 1728.

893 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#126C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic, complemented
3#64104⋊C3C211yesmaximal, characteristic, complemented
4#64103⋊C3C211yesmaximal, characteristic, complemented
5#64102⋊C3C211yesmaximal, characteristic, complemented
6C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
7#64098⋊C3C211yesmaximal, characteristic, complemented
8#64095⋊C3C211yesmaximal, characteristic, complemented
9#64093⋊C3C211yesmaximal, characteristic, complemented
10#64093⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic, complemented
12#64090⋊C3C211yesmaximal, characteristic, complemented
13#64090⋊C3C211yesmaximal, characteristic, complemented
14C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
15#64081⋊C3C211yesmaximal, characteristic, complemented
16#10596180C311yesmaximal, characteristic, complemented
17C3×#5709—31nomaximal
18C2×#638⋊C3C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C4⋊C4×H(3,𝔽3)C2211yescharacteristic
32C4⋊C4×H(3,𝔽3)C2211yescharacteristic
33C22⋊C4×H(3,𝔽3)C2211yescharacteristic
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic
36C42×H(3,𝔽3)C2211yescharacteristic
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
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50#3750⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#126—21no—
54C32×#126D311yescharacteristic, complemented
55C32×#126C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic, complemented
57#64104C2×C311yescharacteristic, complemented
58#64103C2×C311yescharacteristic, complemented
59#64102C2×C311yescharacteristic, complemented
60C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
61#64098C2×C311yescharacteristic, complemented
62#64095C2×C311yescharacteristic, complemented
63#64093C2×C311yescharacteristic, complemented
64#64093C2×C311yescharacteristic, complemented
65#64093C2×C311yescharacteristic, complemented
66#64090C2×C311yescharacteristic, complemented
67#64090C2×C311yescharacteristic, complemented
68C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
69#64081C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#895—31no—
72C3×#894—31no—
73C3×#893—31no—
74C3×D3×C4⋊C4—31no—
75C3×#889—31no—
76C3×#886—31no—
77C3×#884—31no—
78C3×#884—31no—
79C3×#884—31no—
80C3×#67⋊C4—31no—
81C3×#67⋊C4—31no—
82C3×C4×D12—31no—
83C3×#872—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×C4×H(3,𝔽3)C2311yescharacteristic
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#638⋊C3—22no—
95#638⋊C3—22no—
96#638⋊C3—41no—
97C2×(C3⋊Dic3)⋊C3—41no—
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C4⋊((C3⋊D3)⋊C3)—22no—
104C4⋊((C3⋊D3)⋊C3)—22no—
105C4⋊((C3⋊D3)⋊C3)—41no—
106C4×(C3⋊D3)⋊C3—22no—
107C4×(C3⋊D3)⋊C3—22no—
108C4×(C3⋊D3)⋊C3—41no—
109C4×(C3⋊D3)⋊C3—41no—
110C4×(C3⋊D3)⋊C3—41no—
111C3×#553—91no—
112#5709—31no—
113#5709—91no—
114C2×#638C22×C311yescharacteristic
115C2×#638C22×C311yescharacteristic
116C2×#638C22×C311yescharacteristic
117C22×C3⋊Dic3C22×C311yescharacteristic
118C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
119C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
120C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
121C2×C4×C3⋊D3C22×C311yescharacteristic
122C2×C4×C3⋊D3C22×C311yescharacteristic
123C2×C4×C3⋊D3C22×C311yescharacteristic
124C2×C4×C3⋊D3C22×C311yescharacteristic
125C2×C4×C3⋊D3C22×C311yescharacteristic
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C22×C3×Dic3—31no—
130C2×C3×D12—31no—
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C32×C4⋊C4—21no—
139C32×C4⋊C4—21no—
140C32×C4⋊C4—21no—
141C32×C4⋊C4C2×D311yescharacteristic
142C32×C4⋊C4C2×D311yescharacteristic
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C22×C311yescharacteristic
145C32×C4⋊C4C22×C311yescharacteristic
146C32×C4⋊C4C22×C311yescharacteristic
147C32×C22⋊C4—21no—
148C32×C22⋊C4—21no—
149C32×C22⋊C4—21no—
150C32×C22⋊C4C2×D311yescharacteristic
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C2×D311yescharacteristic
153C32×C22⋊C4C22×C311yescharacteristic
154C32×C22⋊C4C22×C311yescharacteristic
155C32×C22⋊C4C22×C311yescharacteristic
156C32×C42—21no—
157C32×C42C2×D311yescharacteristic
158C32×C42C22×C311yescharacteristic
159#3752C22×C311yescharacteristic
160#3752C22×C311yescharacteristic
161#3752C22×C311yescharacteristic
162#3752C22×C311yescharacteristic
163#3752C22×C311yescharacteristic
164#3752C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166C4⋊(C3⋊Dic3)C22×C311yescharacteristic
167C4⋊(C3⋊Dic3)C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170#3750C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172#3750C22×C311yescharacteristic
173C4×C3⋊Dic3C22×C311yescharacteristic
174C4×C3⋊Dic3C22×C311yescharacteristic
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×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—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)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#4112yes—
204C4×H(3,𝔽3)—21no—
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#4112yes—
215C3×#126—31no—
216C3×#126—31no—
217C3×#126—61no—
218C3×#126—91no—
219C3×#126C3×D311yescharacteristic
220C3×#125—91no—
221C3×#123—91no—
222C3×#123—91no—
223C3×#121—91no—
224C3×#121—91no—
225C3×#121—91no—
226C3×#121—91no—
227C3×C4×D4—91no—
228C3×C4×D4—91no—
229C3×C4×D4—91no—
230C3×C4×D4—91no—
231C3×#117—91no—
232C2×C3×C4⋊C4—91no—
233#898—31no—
234#898—91no—
235#895—31no—
236#895—91no—
237#894—31no—
238#894—91no—
239#893—31no—
240#893—91no—
241D3×C4⋊C4—31no—
242D3×C4⋊C4—91no—
243#889—31no—
244#889—91no—
245#886—31no—
246#886—91no—
247#884—31no—
248#884—31no—
249#884—31no—
250#884—91no—
251#884—91no—
252#884—91no—
253#67⋊C4—31no—
254#67⋊C4—31no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257C4×D12—31no—
258C4×D12—91no—
259#872—31no—
260#872—91no—
261C23×C32—21no—
262C23×C32C22×D311yescharacteristic
263C23×C32C23×C311yescharacteristic
264C22×C3⋊D3C23×C311yescharacteristic
265C22×C3⋊D3C23×C311yescharacteristic
266C22×C3⋊D3C23×C311yescharacteristic
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C23×C311yescharacteristic
283C2×C32×C4C23×C311yescharacteristic
284C2×C32×C4C23×C311yescharacteristic
285C2×C32×C4C23×C311yescharacteristic
286C2×C32×C4C23×C311yescharacteristic
287C2×C32×C4C23×C311yescharacteristic
288#638—22no—
289#638—22no—
290#638—41no—
291C2×C3⋊Dic3—41no—
292C2×C3⋊Dic3C23×C311yescharacteristic
293C2×C3⋊Dic3C23×C311yescharacteristic
294C2×C3⋊Dic3C23×C311yescharacteristic
295C2×C3⋊Dic3C23×C311yescharacteristic
296C2×C3⋊Dic3C23×C311yescharacteristic
297C4⋊(C3⋊D3)—22no—
298C4⋊(C3⋊D3)—22no—
299C4⋊(C3⋊D3)—41no—
300C4×C3⋊D3—22no—
301C4×C3⋊D3—22no—
302C4×C3⋊D3—41no—
303C4×C3⋊D3—41no—
304C4×C3⋊D3—41no—
305C3×#67—62no—
306C3×#67—62no—
307C3×#67—121no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—121no—
314C3×D12—62no—
315C3×D12—62no—
316C3×D12—121no—
317C3×C4×D3—62no—
318C3×C4×D3—62no—
319C3×C4×D3—121no—
320C3×C4×D3—121no—
321C3×C4×D3—121no—
322#553—91noSylow
323C2×H(3,𝔽3)—41no—
324C2×H(3,𝔽3)C2×#4111yescharacteristic
325C2×H(3,𝔽3)C2×#4111yescharacteristic
326C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
327(C3⋊D3)⋊C3—22no—
328(C3⋊D3)⋊C3—41no—
329(C3⋊D3)⋊C3—41no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C22×C3×C4—91no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—31no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C22×Dic3—31no—
349C22×Dic3—91no—
350C2×D12—31no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—91no—
354C2×D12—91no—
355C2×D12—91no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—91no—
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4—91no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C4⋊C4C2×C3×D311yescharacteristic
383C3×C4⋊C4C2×C3×D311yescharacteristic
384C3×C4⋊C4C2×C3×D311yescharacteristic
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C22⋊C4—91no—
400C3×C22⋊C4—91no—
401C3×C22⋊C4C2×C3×D311yescharacteristic
402C3×C22⋊C4C2×C3×D311yescharacteristic
403C3×C22⋊C4C2×C3×D311yescharacteristic
404C3×C42—31no—
405C3×C42—31no—
406C3×C42—61no—
407C3×C42—91no—
408C3×C42—91no—
409C3×C42C2×C3×D311yescharacteristic
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—91no—
418(C2×D3)⋊C4—91no—
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—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—91no—
427C4⋊Dic3—91no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
431Dic3⋊C4—31no—
432Dic3⋊C4—31no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32C23×D311yescharacteristic
453C22×C32C24×C311yescharacteristic
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
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⋊D3C3×#4112yes—
463C2×C3×D3—32no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4—21no—
477C32×C4—21no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—21no—
484C32×C4—41no—
485C32×C4—41no—
486C32×C4—41no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4—41no—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3C3×#4112yes—
495C3×Dic3—32no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500#126—91no—
501#126(C3⋊D3)⋊C311yescharacteristic, complemented
502#125—91no—
503#123—91no—
504#123—91no—
505#121—91no—
506#121—91no—
507#121—91no—
508#121—91no—
509C4×D4—91no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—91no—
513#117—91no—
514C2×C4⋊C4—91no—
515H(3,𝔽3)#55311yescharacteristic, complemented, Sylow
516C23×C3—31no—
517C23×C3—31no—
518C23×C3—61no—
519C23×C3—91no—
520C23×C3—91no—
521C23×C3—91no—
522C23×C3C22×C3×D311yescharacteristic
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—31no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C3×D4—182no—
530C3×D4—182no—
531C3×D4—182no—
532C3×D4—182no—
533C3×D4—361no—
534C3×D4—361no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—182no—
559C2×C3×C4—182no—
560C2×C3×C4—361no—
561C2×C3×C4—361no—
562C2×C3×C4—361no—
563C2×C3×C4—361no—
564C2×C3×C4C22×C3×D311yescharacteristic
565C2×C3×C4C22×C3×D311yescharacteristic
566C2×C3×C4C22×C3×D311yescharacteristic
567C2×C3×C4C22×C3×D311yescharacteristic
568C2×C3×C4C22×C3×D311yescharacteristic
569C2×C3×C4C22×C3×D311yescharacteristic
570#67—62no—
571#67—62no—
572#67—121no—
573#67—182no—
574#67—182no—
575#67—361no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—121no—
587C2×Dic3—361no—
588D12—62no—
589D12—62no—
590D12—121no—
591D12—182no—
592D12—182no—
593D12—361no—
594C4×D3—62no—
595C4×D3—62no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—121no—
599C4×D3—182no—
600C4×D3—182no—
601C4×D3—361no—
602C4×D3—361no—
603C4×D3—361no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—41no—
608C2×C32—41no—
609C2×C32—81no—
610C2×C32D3×#4111yescharacteristic
611C2×C32D3×#4111yescharacteristic
612C2×C32#100911yescharacteristic
613C2×C32C2×C3×#4111yescharacteristic
614C2×C32C2×C3×#4111yescharacteristic
615C2×C32C3×H(5,𝔽2)11yescharacteristic
616C3⋊D3—22no—
617C3⋊D3—41no—
618C3⋊D3—41no—
619C3×D3—62no—
620C3×D3—121no—
621C3×D3—121no—
622C2×D4—91no—
623C2×D4—91no—
624C2×D4—91no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—91no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
642C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
643C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
644C22⋊C4—91no—
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
652C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
653C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
654C42—91no—
655C42—91no—
656C42C2×(C3⋊D3)⋊C311yescharacteristic
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—31no—
661C22×C3—31no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—92no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3C23×C3×D311yescharacteristic
682C2×D3—32no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—92no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—92no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4—181no—
729Dic3—32no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—92no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739C32—21no—
740C32#570911yescharacteristic, complemented
741C32C3×#55311yescharacteristic, complemented
742C23—91no—
743C23—91no—
744C23—91no—
745C23C22×(C3⋊D3)⋊C311yescharacteristic
746D4—182no—
747D4—182no—
748D4—182no—
749D4—182no—
750D4—361no—
751D4—361no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—182no—
758C2×C4—182no—
759C2×C4—361no—
760C2×C4—361no—
761C2×C4—361no—
762C2×C4—361no—
763C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
764C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
765C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
766C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
767C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
768C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
769C2×C3—31no—
770C2×C3—31no—
771C2×C3—31no—
772C2×C3—31no—
773C2×C3—31no—
774C2×C3—31no—
775C2×C3—41no—
776C2×C3—61no—
777C2×C3—61no—
778C2×C3—61no—
779C2×C3—121no—
780C2×C3—121no—
781C2×C3—182no—
782C2×C3—241no—
783C2×C3—361no—
784C2×C3—361no—
785C2×C3C3×D3×#4111yescharacteristic
786C2×C3C3×D3×#4111yescharacteristic
787C2×C3C3×#100911yescharacteristic
788D3—62no—
789D3—121no—
790D3—121no—
791D3—182no—
792D3—361no—
793D3—361no—
794C22—21no—
795C22—21no—
796C22—21no—
797C22—92no—
798C22—181no—
799C22—181no—
800C22—181no—
801C22—181no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—181no—
806C22C23×(C3⋊D3)⋊C311yescharacteristic
807C4—21no—
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—92no—
814C4—181no—
815C4—181no—
816C4—181no—
817C4—181no—
818C3—31no—
819C3—31no—
820C3—61no—
821C3C3×#570911yescharacteristic
822C2—41no—
823C2—182no—
824C2—361no—
825C2—361no—
826C2#41×(C3⋊D3)⋊C311yescharacteristic
827C2#41×(C3⋊D3)⋊C311yescharacteristic
828C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#126C2
hypercenter#126(C3⋊D3)⋊C3
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#126C2semidirect
2. #64107⋊C3C2semidirect
3. #64104⋊C3C2semidirect
4. #64103⋊C3C2semidirect
5. #64102⋊C3C2semidirect
6. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
7. #64098⋊C3C2semidirect
8. #64095⋊C3C2semidirect
9. #64093⋊C3C2semidirect
10. #64093⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #64090⋊C3C2semidirect
13. #64090⋊C3C2semidirect
14. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
15. #64081⋊C3C2semidirect
16. #10596180C3semidirect
54. C32×#126D3semidirect
55. C32×#126C2×C3semidirect
56. #64107C2×C3semidirect
57. #64104C2×C3semidirect
58. #64103C2×C3semidirect
59. #64102C2×C3semidirect
60. C4⋊C4×C3⋊D3C2×C3semidirect
61. #64098C2×C3semidirect
62. #64095C2×C3semidirect
63. #64093C2×C3semidirect
64. #64093C2×C3semidirect
65. #64093C2×C3semidirect
66. #64090C2×C3semidirect
67. #64090C2×C3semidirect
68. C4×C4⋊(C3⋊D3)C2×C3semidirect
69. #64081C2×C3semidirect
501. #126(C3⋊D3)⋊C3semidirect
515. H(3,𝔽3)#553semidirect
740. C32#5709semidirect
741. C32C3×#553semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1262
#64107⋊C32
#64104⋊C32
#64103⋊C32
#64102⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#64095⋊C32
#64093⋊C32
#64090⋊C32
C4×C4⋊((C3⋊D3)⋊C3)2
#64081⋊C32
#105961803
C3×#57093