Finite Group Databasebeta

← #10596002⋊C3 #13152509

Subgroups — #10596002⋊C3 #13152509

Order 1728.

825 conjugacy classes of subgroups.

The subgroup lattice has 748 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
3C2×#3750⋊C3C211yesmaximal, characteristic, complemented
4#64107⋊C3C211yesmaximal, characteristic, complemented
5#64105⋊C3C211yesmaximal, characteristic, complemented
6#64098⋊C3C211yesmaximal, characteristic, complemented
7#64098⋊C3C211yesmaximal, characteristic, complemented
8#64095⋊C3C211yesmaximal, characteristic
9#64090⋊C3C211yesmaximal, characteristic
10#64087⋊C3C211yesmaximal, characteristic, complemented
11#64086⋊C3C211yesmaximal, characteristic, complemented
12#11721387C211yesmaximal, characteristic, complemented
13#64081⋊C3C211yesmaximal, characteristic, complemented
14#64079⋊C3C211yesmaximal, characteristic, complemented
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10596002C311yesmaximal, characteristic, complemented
17C3×#5531—31nomaximal
18C22×C4×H(3,𝔽3)C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C22⋊C4×H(3,𝔽3)C2211yescharacteristic
27C22⋊C4×H(3,𝔽3)C2211yescharacteristic
28C42×H(3,𝔽3)C2211yescharacteristic
29C42×H(3,𝔽3)C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31#3752⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
39#3750⋊C3C2211yescharacteristic
40#3750⋊C3C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#117—21no—
54C32×#117D311yescharacteristic, complemented
55C32×#117C2×C311yescharacteristic, complemented
56#64138C2×C311yescharacteristic
57C2×#3750C2×C311yescharacteristic, complemented
58#64107C2×C311yescharacteristic, complemented
59#64105C2×C311yescharacteristic, complemented
60#64098C2×C311yescharacteristic, complemented
61#64098C2×C311yescharacteristic, complemented
62#64095C2×C311yescharacteristic
63#64090C2×C311yescharacteristic
64#64087C2×C311yescharacteristic, complemented
65#64086C2×C311yescharacteristic, complemented
66#64085C2×C311yescharacteristic, complemented
67#64081C2×C311yescharacteristic, complemented
68#64079C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×#929—31no—
71C2×C3×Dic3⋊C4—31no—
72C3×#898—31no—
73C3×#896—31no—
74C3×#889—31no—
75C3×#889—31no—
76C3×#886—31no—
77C3×#67⋊C4—31no—
78C3×#878—31no—
79C3×#877—31no—
80C3×#876—31no—
81C3×#872—31no—
82C3×#870—31no—
83C3×C4×Dic6—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C2×C4×H(3,𝔽3)—22no—
87C2×C4×H(3,𝔽3)C2311yescharacteristic
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
93#638⋊C3—22no—
94C2×(C3⋊Dic3)⋊C3—22no—
95C2×(C3⋊Dic3)⋊C3—22no—
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
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—
104#634⋊C3—22no—
105C3×#552—91no—
106#5531—31no—
107#5531—91no—
108C22×C32×C4—21no—
109C22×C32×C4C2×D311yescharacteristic
110C22×C32×C4C22×C311yescharacteristic
111C2×#638C22×C311yescharacteristic
112C22×C3⋊Dic3C22×C311yescharacteristic
113C22×C3⋊Dic3C22×C311yescharacteristic
114C2×C4×C3⋊D3C22×C311yescharacteristic
115C2×#634C22×C311yescharacteristic
116C2×C3×#67—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—31no—
119C2×C3×C4×D3—31no—
120C2×C3×Dic6—31no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C22×C311yescharacteristic
126C32×C4⋊C4C22×C311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4C2×D311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131C32×C22⋊C4C22×C311yescharacteristic
132C32×C22⋊C4C22×C311yescharacteristic
133C32×C42—21no—
134C32×C42—21no—
135C32×C42C2×D311yescharacteristic
136C32×C42C2×D311yescharacteristic
137C32×C42C22×C311yescharacteristic
138C32×C42C22×C311yescharacteristic
139#3757C22×C311yescharacteristic
140#3752C22×C311yescharacteristic
141#3752C22×C311yescharacteristic
142#3752C22×C311yescharacteristic
143#3752C22×C311yescharacteristic
144#3752C22×C311yescharacteristic
145C4⋊(C3⋊Dic3)C22×C311yescharacteristic
146C4⋊(C3⋊Dic3)C22×C311yescharacteristic
147C4⋊(C3⋊Dic3)C22×C311yescharacteristic
148#3750C22×C311yescharacteristic
149#3750C22×C311yescharacteristic
150#3750C22×C311yescharacteristic
151#3750C22×C311yescharacteristic
152#3750C22×C311yescharacteristic
153#3750C22×C311yescharacteristic
154#3750C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156#3750C22×C311yescharacteristic
157#3750C22×C311yescharacteristic
158#3750C22×C311yescharacteristic
159C4×C3⋊Dic3C22×C311yescharacteristic
160C4×C3⋊Dic3C22×C311yescharacteristic
161C4×C3⋊Dic3C22×C311yescharacteristic
162C3×#217—31no—
163C3×(C2×D3)⋊C4—31no—
164C3×(C2×D3)⋊C4—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×Dic3⋊C4—31no—
172C3×Dic3⋊C4—31no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—31no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×C4×Dic3—31no—
183C3×C4×Dic3—31no—
184C3×C4×Dic3—31no—
185C22×H(3,𝔽3)—21no—
186C22×H(3,𝔽3)—21no—
187C22×H(3,𝔽3)#4112yes—
188C22×H(3,𝔽3)C2411yescharacteristic
189C2×(C3⋊D3)⋊C3—21no—
190C2×(C3⋊D3)⋊C3—21no—
191C2×(C3⋊D3)⋊C3—21no—
192C4×H(3,𝔽3)—21no—
193C4×H(3,𝔽3)—21no—
194C4×H(3,𝔽3)—21no—
195C4×H(3,𝔽3)—21no—
196C4×H(3,𝔽3)—21no—
197C4×H(3,𝔽3)—21no—
198(C3⋊Dic3)⋊C3—21no—
199(C3⋊Dic3)⋊C3—21no—
200(C3⋊Dic3)⋊C3—21no—
201(C3⋊Dic3)⋊C3—21no—
202(C3⋊Dic3)⋊C3—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3#4112yes—
205C3×#126—91no—
206C3×#126—91no—
207C3×#125—91no—
208C3×#125—91no—
209C3×#125—91no—
210C3×#123—91no—
211C3×#123—91no—
212C3×C22⋊Q8—91no—
213C3×C22⋊Q8—91no—
214C3×C4×Q8—91no—
215C3×C4×D4—91no—
216C3×#117—31no—
217C3×#117—31no—
218C3×#117—61no—
219C3×#117—91no—
220C3×#117—91no—
221C3×#117C3×D311yescharacteristic
222C2×C3×C4⋊C4—91no—
223#929—31no—
224#929—91no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—91no—
227#898—31no—
228#898—91no—
229#896—31no—
230#896—91no—
231#889—31no—
232#889—31no—
233#889—91no—
234#889—91no—
235#886—31no—
236#886—91no—
237#67⋊C4—31no—
238#67⋊C4—91no—
239#878—31no—
240#878—91no—
241#877—31no—
242#877—91no—
243#876—31no—
244#876—91no—
245#872—31no—
246#872—91no—
247#870—31no—
248#870—91no—
249C4×Dic6—31no—
250C4×Dic6—91no—
251C23×C32—21no—
252C23×C32C22×D311yescharacteristic
253C23×C32C23×C311yescharacteristic
254C22×C3⋊D3C23×C311yescharacteristic
255C22×C3×D3—31no—
256C2×C32×C4—24no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272C2×C32×C4C23×C311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274C2×C32×C4C23×C311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C32×C4C23×C311yescharacteristic
277#638—22no—
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3C23×C311yescharacteristic
281C2×C3⋊Dic3C23×C311yescharacteristic
282C2×C3⋊Dic3C23×C311yescharacteristic
283C2×C3⋊Dic3C23×C311yescharacteristic
284C2×C3⋊Dic3C23×C311yescharacteristic
285C2×C3⋊Dic3C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C4×C3⋊D3—22no—
288#634—22no—
289C3×#67—62no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—62no—
299C3×C4×D3—62no—
300C3×Dic6—62no—
301#552—91noSylow
302C2×H(3,𝔽3)—22no—
303C2×H(3,𝔽3)C2×#4111yescharacteristic
304C2×H(3,𝔽3)C2×#4111yescharacteristic
305C2×H(3,𝔽3)2−1+411yescharacteristic
306(C3⋊D3)⋊C3—41no—
307C2×C3×Q8—91no—
308C2×C3×D4—91no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—91no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4C2×C3×D311yescharacteristic
316C2×#67—31no—
317C2×#67—91no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—91no—
321C22×Dic3—91no—
322C2×C4×D3—31no—
323C2×C4×D3—91no—
324C2×Dic6—31no—
325C2×Dic6—91no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4—91no—
337C3×C4⋊C4—91no—
338C3×C4⋊C4—91no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4C2×C3×D311yescharacteristic
347C3×C4⋊C4C2×C3×D311yescharacteristic
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4C2×C3×D311yescharacteristic
361C3×C22⋊C4C2×C3×D311yescharacteristic
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—91no—
369C3×C42—91no—
370C3×C42—91no—
371C3×C42C2×C3×D311yescharacteristic
372C3×C42C2×C3×D311yescharacteristic
373#217—31no—
374#217—91no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—91no—
389C4⋊Dic3—91no—
390C4⋊Dic3—91no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—22no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32#23512yes—
428C22×C32C3×#4112yes—
429C22×C32C23×D311yescharacteristic
430C22×C32C24×C311yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C2×C3×D3—61no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—41no—
452C32×C4—41no—
453C32×C4—41no—
454C32×C4—41no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3C3×#4112yes—
462C3×Dic3—32no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469#126—91no—
470#126—91no—
471#125—91no—
472#125—91no—
473#125—91no—
474#123—91no—
475#123—91no—
476C22⋊Q8—91no—
477C22⋊Q8—91no—
478C4×Q8—91no—
479C4×D4—91no—
480#117—91no—
481#117—91no—
482#117(C3⋊D3)⋊C311yescharacteristic, complemented
483C2×C4⋊C4—91no—
484H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
485C23×C3—31no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—91no—
489C23×C3C22×C3×D311yescharacteristic
490C22×D3—31no—
491C22×D3—91no—
492C3×Q8—182no—
493C3×D4—182no—
494C2×C3×C4—22no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—182no—
524C2×C3×C4—182no—
525C2×C3×C4—182no—
526C2×C3×C4C22×C3×D311yescharacteristic
527C2×C3×C4C22×C3×D311yescharacteristic
528C2×C3×C4C22×C3×D311yescharacteristic
529C2×C3×C4C22×C3×D311yescharacteristic
530C2×C3×C4C22×C3×D311yescharacteristic
531C2×C3×C4C22×C3×D311yescharacteristic
532#67—62no—
533#67—182no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—91no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—182no—
551C2×Dic3—182no—
552C4×D3—62no—
553C4×D3—182no—
554Dic6—62no—
555Dic6—182no—
556C2×C32—22no—
557C2×C32—22no—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—21no—
561C2×C32—42no—
562C2×C32C2×#23511yescharacteristic
563C2×C32D3×#4111yescharacteristic
564C2×C32#101011yescharacteristic
565C2×C32C2×C3×#4111yescharacteristic
566C2×C32C2×C3×#4111yescharacteristic
567C2×C32C3×2−1+411yescharacteristic
568C3⋊D3—41no—
569C3×D3—121no—
570C2×Q8—91no—
571C2×D4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—91no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
591C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
599C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
600C42—91no—
601C42—91no—
602C42—91no—
603C42C2×(C3⋊D3)⋊C311yescharacteristic
604C42C2×(C3⋊D3)⋊C311yescharacteristic
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—31no—
608C22×C3—31no—
609C22×C3—32no—
610C22×C3—32no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3C3×#23512yes—
623C22×C3C23×C3×D311yescharacteristic
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—181no—
628C2×D3—181no—
629C2×D3—181no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—92no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659C3×C4—181no—
660C3×C4—181no—
661Dic3—32no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—61no—
668Dic3—92no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675C32—21no—
676C32#553111yescharacteristic, complemented
677C32C3×#55211yescharacteristic, complemented
678C23—91no—
679C23C22×(C3⋊D3)⋊C311yescharacteristic
680Q8—182no—
681D4—182no—
682C2×C4—22no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—91no—
690C2×C4—182no—
691C2×C4—182no—
692C2×C4—182no—
693C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
694C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
695C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
696C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
697C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
698C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
699C2×C3—22no—
700C2×C3—31no—
701C2×C3—31no—
702C2×C3—31no—
703C2×C3—31no—
704C2×C3—31no—
705C2×C3—31no—
706C2×C3—62no—
707C2×C3—62no—
708C2×C3—61no—
709C2×C3—61no—
710C2×C3—61no—
711C2×C3—122no—
712C2×C3—361no—
713C2×C3C2×C3×#23511yescharacteristic
714C2×C3C3×D3×#4111yescharacteristic
715C2×C3C3×#101011yescharacteristic
716D3—121no—
717D3—361no—
718C22—21no—
719C22—21no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22#3828⋊C312yes—
724C22C23×(C3⋊D3)⋊C311yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—92no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—181no—
738C3—31no—
739C3—31no—
740C3—61no—
741C3C3×#553111yescharacteristic
742C2—22no—
743C2—361no—
744C2C2×#3828⋊C311yescharacteristic
745C2#41×(C3⋊D3)⋊C311yescharacteristic
746C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#117C2
prime radicalC2×#638⋊C3C22
hypercenter#117(C3⋊D3)⋊C3
hypocenterC32C3×#552
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
3. C2×#3750⋊C3C2semidirect
4. #64107⋊C3C2semidirect
5. #64105⋊C3C2semidirect
6. #64098⋊C3C2semidirect
7. #64098⋊C3C2semidirect
10. #64087⋊C3C2semidirect
11. #64086⋊C3C2semidirect
12. #11721387C2semidirect
13. #64081⋊C3C2semidirect
14. #64079⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10596002C3semidirect
54. C32×#117D3semidirect
55. C32×#117C2×C3semidirect
57. C2×#3750C2×C3semidirect
58. #64107C2×C3semidirect
59. #64105C2×C3semidirect
60. #64098C2×C3semidirect
61. #64098C2×C3semidirect
64. #64087C2×C3semidirect
65. #64086C2×C3semidirect
66. #64085C2×C3semidirect
67. #64081C2×C3semidirect
68. #64079C2×C3semidirect
69. C4×#634C2×C3semidirect
482. #117(C3⋊D3)⋊C3semidirect
484. H(3,𝔽3)#552semidirect
676. C32#5531semidirect
677. C32C3×#552semidirect

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×#3750⋊C32
#64107⋊C32
#64105⋊C32
#64098⋊C32
#64095⋊C32
#64090⋊C32
#64087⋊C32
#64086⋊C32
#117213872
#64081⋊C32
#64079⋊C32
C4×#634⋊C32
#105960023
C3×#55313