Finite Group Databasebeta

← #10596121⋊C3 #13153039

Subgroups — #10596121⋊C3 #13153039

Order 1728.

827 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#123C211yesmaximal, characteristic
2#64144⋊C3C211yesmaximal, characteristic
3D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic
4#64135⋊C3C211yesmaximal, characteristic, complemented
5C2×#3750⋊C3C211yesmaximal, characteristic, complemented
6#64099⋊C3C211yesmaximal, characteristic, complemented
7#64098⋊C3C211yesmaximal, characteristic, complemented
8#64098⋊C3C211yesmaximal, characteristic, complemented
9#64096⋊C3C211yesmaximal, characteristic, complemented
10#64088⋊C3C211yesmaximal, characteristic, complemented
11#64088⋊C3C211yesmaximal, characteristic, complemented
12#64087⋊C3C211yesmaximal, characteristic, complemented
13#64087⋊C3C211yesmaximal, characteristic, complemented
14#64086⋊C3C211yesmaximal, characteristic, complemented
15#64086⋊C3C211yesmaximal, characteristic, complemented
16#10596121C311yesmaximal, characteristic, complemented
17C3×#5650—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊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
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#3757⋊C3C2211yescharacteristic
30#3757⋊C3C2211yescharacteristic
31#3757⋊C3C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
38#3750⋊C3C2211yescharacteristic
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
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
49C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#123—21no—
54C32×#123D311yescharacteristic
55C32×#123C2×C311yescharacteristic
56#64144C2×C311yescharacteristic
57D4×C3⋊Dic3C2×C311yescharacteristic
58#64135C2×C311yescharacteristic, complemented
59C2×#3750C2×C311yescharacteristic, complemented
60#64099C2×C311yescharacteristic, complemented
61#64098C2×C311yescharacteristic, complemented
62#64098C2×C311yescharacteristic, complemented
63#64096C2×C311yescharacteristic, complemented
64#64088C2×C311yescharacteristic, complemented
65#64088C2×C311yescharacteristic, complemented
66#64087C2×C311yescharacteristic, complemented
67#64087C2×C311yescharacteristic, complemented
68#64086C2×C311yescharacteristic, complemented
69#64086C2×C311yescharacteristic, complemented
70C3×#935—31no—
71C3×D4×Dic3—31no—
72C3×#926—31no—
73C2×C3×Dic3⋊C4—31no—
74C3×#890—31no—
75C3×#889—31no—
76C3×#889—31no—
77C3×#887—31no—
78C3×#879—31no—
79C3×#879—31no—
80C3×#878—31no—
81C3×#878—31no—
82C3×#877—31no—
83C3×#877—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86D4×H(3,𝔽3)—22no—
87C2×C4×H(3,𝔽3)—22no—
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×(C3⋊Dic3)⋊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
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104#634⋊C3—22no—
105C3×#552—91no—
106#5650—31no—
107#5650—91no—
108C2×C32×D4—21no—
109C2×C32×D4C2×D311yescharacteristic
110C2×C32×D4C22×C311yescharacteristic
111C22×C32×C4—21no—
112C22×C32×C4C2×D311yescharacteristic
113C22×C32×C4C22×C311yescharacteristic
114C22×C3⋊Dic3C22×C311yescharacteristic
115C22×C3⋊Dic3C22×C311yescharacteristic
116C22×C3⋊Dic3C22×C311yescharacteristic
117C2×#634C22×C311yescharacteristic
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C2×C3×Dic6—31no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C22×C311yescharacteristic
127C32×C4⋊C4C22×C311yescharacteristic
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C22⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C22⋊C4C22×C311yescharacteristic
135C32×C22⋊C4C22×C311yescharacteristic
136C32×C22⋊C4C22×C311yescharacteristic
137#3757C22×C311yescharacteristic
138#3757C22×C311yescharacteristic
139#3757C22×C311yescharacteristic
140#3757C22×C311yescharacteristic
141#3757C22×C311yescharacteristic
142C4⋊(C3⋊Dic3)C22×C311yescharacteristic
143C4⋊(C3⋊Dic3)C22×C311yescharacteristic
144C4⋊(C3⋊Dic3)C22×C311yescharacteristic
145C4⋊(C3⋊Dic3)C22×C311yescharacteristic
146#3750C22×C311yescharacteristic
147#3750C22×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
156C4×C3⋊Dic3C22×C311yescharacteristic
157C4×C3⋊Dic3C22×C311yescharacteristic
158C4×C3⋊Dic3C22×C311yescharacteristic
159C4×C3⋊Dic3C22×C311yescharacteristic
160C4×C3⋊Dic3C22×C311yescharacteristic
161C3×#217—31no—
162C3×#217—31no—
163C3×#217—31no—
164C3×#217—31no—
165C3×#217—31no—
166C3×C4⋊Dic3—31no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—31no—
170C3×Dic3⋊C4—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×C4×Dic3—31no—
181C3×C4×Dic3—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)—21no—
188C22×H(3,𝔽3)—21no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)#4112yes—
191C22×H(3,𝔽3)C2411yescharacteristic
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—
197(C3⋊Dic3)⋊C3—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—31no—
211C3×#123—31no—
212C3×#123—61no—
213C3×#123—91no—
214C3×#123C3×D311yescharacteristic
215C3×C22⋊Q8—91no—
216C3×C22⋊Q8—91no—
217C3×C4×Q8—91no—
218C3×C4×D4—91no—
219C3×#117—91no—
220C3×#117—91no—
221C3×#117—91no—
222C2×C3×C4⋊C4—91no—
223#935—31no—
224#935—91no—
225D4×Dic3—31no—
226D4×Dic3—91no—
227#926—31no—
228#926—91no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—91no—
231#890—31no—
232#890—91no—
233#889—31no—
234#889—31no—
235#889—91no—
236#889—91no—
237#887—31no—
238#887—91no—
239#879—31no—
240#879—31no—
241#879—91no—
242#879—91no—
243#878—31no—
244#878—31no—
245#878—91no—
246#878—91no—
247#877—31no—
248#877—31no—
249#877—91no—
250#877—91no—
251C23×C32—21no—
252C23×C32—21no—
253C23×C32C22×D311yescharacteristic
254C23×C32C22×D311yescharacteristic
255C23×C32C23×C311yescharacteristic
256C23×C32C23×C311yescharacteristic
257C32×D4—22no—
258C32×D4—22no—
259C32×D4—42no—
260C2×C32×C4—22no—
261C2×C32×C4—22no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—42no—
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274C2×C32×C4C23×C311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C32×C4C23×C311yescharacteristic
277C2×C32×C4C23×C311yescharacteristic
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3C23×C311yescharacteristic
282C2×C3⋊Dic3C23×C311yescharacteristic
283C2×C3⋊Dic3C23×C311yescharacteristic
284C2×C3⋊Dic3C23×C311yescharacteristic
285C2×C3⋊Dic3C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C311yescharacteristic
288C2×C3⋊Dic3C23×C311yescharacteristic
289#634—22no—
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—31no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—62no—
301C3×Dic6—62no—
302#552—91noSylow
303C2×H(3,𝔽3)—22no—
304C2×H(3,𝔽3)—41no—
305C2×H(3,𝔽3)C2×#4111yescharacteristic
306C2×H(3,𝔽3)C2×#4111yescharacteristic
307C2×H(3,𝔽3)2−1+411yescharacteristic
308C2×C3×Q8—91no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4C2×C3×D311yescharacteristic
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×C3×C4C2×C3×D311yescharacteristic
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C22×Dic3—91no—
326C2×Dic6—31no—
327C2×Dic6—91no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
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⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4C2×C3×D311yescharacteristic
349C3×C4⋊C4C2×C3×D311yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4C2×C3×D311yescharacteristic
365C3×C22⋊C4C2×C3×D311yescharacteristic
366C3×C22⋊C4C2×C3×D311yescharacteristic
367C3×C42—91no—
368C3×C42—91no—
369C3×C42—91no—
370C3×C42—91no—
371C3×C42—91no—
372#217—31no—
373#217—31no—
374#217—31no—
375#217—31no—
376#217—31no—
377#217—91no—
378#217—91no—
379#217—91no—
380#217—91no—
381#217—91no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—91no—
387C4⋊Dic3—91no—
388C4⋊Dic3—91no—
389C4⋊Dic3—91no—
390Dic3⋊C4—31no—
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—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C4×Dic3—91no—
419C4×Dic3—91no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32#23712yes—
438C22×C32C3×#4112yes—
439C22×C32C23×D311yescharacteristic
440C22×C32C24×C311yescharacteristic
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—
455C32×C4—41no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3⋊Dic3C3×#4112yes—
464C3×Dic3—32no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472#126—91no—
473#126—91no—
474#125—91no—
475#125—91no—
476#125—91no—
477#123—91no—
478#123(C3⋊D3)⋊C311yescharacteristic
479C22⋊Q8—91no—
480C22⋊Q8—91no—
481C4×Q8—91no—
482C4×D4—91no—
483#117—91no—
484#117—91no—
485#117—91no—
486C2×C4⋊C4—91no—
487H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
488C23×C3—31no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3C22×C3×D311yescharacteristic
495C23×C3C22×C3×D311yescharacteristic
496C3×Q8—182no—
497C3×D4—22no—
498C3×D4—62no—
499C3×D4—62no—
500C3×D4—122no—
501C2×C3×C4—22no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—122no—
528C2×C3×C4—182no—
529C2×C3×C4—182no—
530C2×C3×C4—182no—
531C2×C3×C4C22×C3×D311yescharacteristic
532C2×C3×C4C22×C3×D311yescharacteristic
533C2×C3×C4C22×C3×D311yescharacteristic
534C2×C3×C4C22×C3×D311yescharacteristic
535C2×C3×C4C22×C3×D311yescharacteristic
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—62no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—182no—
556C2×Dic3—182no—
557C2×Dic3—182no—
558Dic6—62no—
559Dic6—182no—
560C2×C32—22no—
561C2×C32—22no—
562C2×C32—21no—
563C2×C32—21no—
564C2×C32—21no—
565C2×C32—42no—
566C2×C32—41no—
567C2×C32—41no—
568C2×C32—81no—
569C2×C32C2×#23711yescharacteristic
570C2×C32D3×#4111yescharacteristic
571C2×C32#101011yescharacteristic
572C2×C32C2×C3×#4111yescharacteristic
573C2×C32C2×C3×#4111yescharacteristic
574C2×C32C3×2−1+411yescharacteristic
575C2×Q8—91no—
576C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
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⋊C4—91no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—91no—
595C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
596C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
603C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
604C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
605C42—91no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42—91no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—31no—
616C22×C3—31no—
617C22×C3—32no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C3×#23712yes—
637C22×C3C23×C3×D311yescharacteristic
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—92no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—181no—
660C3×C4—181no—
661C3×C4—181no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—181no—
665C3×C4—181no—
666Dic3—32no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—92no—
675Dic3—181no—
676Dic3—181no—
677Dic3—181no—
678Dic3—181no—
679Dic3—181no—
680Dic3—181no—
681Dic3—181no—
682C32—21no—
683C32#565011yescharacteristic, complemented
684C32C3×#55211yescharacteristic, complemented
685C23C22×(C3⋊D3)⋊C311yescharacteristic
686C23C22×(C3⋊D3)⋊C311yescharacteristic
687Q8—182no—
688D4—22no—
689C2×C4—22no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—182no—
699C2×C4—182no—
700C2×C4—182no—
701C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
702C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
703C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
704C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
705C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
706C2×C3—22no—
707C2×C3—31no—
708C2×C3—31no—
709C2×C3—31no—
710C2×C3—31no—
711C2×C3—31no—
712C2×C3—31no—
713C2×C3—41no—
714C2×C3—62no—
715C2×C3—62no—
716C2×C3—61no—
717C2×C3—61no—
718C2×C3—61no—
719C2×C3—122no—
720C2×C3—121no—
721C2×C3—121no—
722C2×C3—241no—
723C2×C3C2×C3×#23711yescharacteristic
724C2×C3C3×D3×#4111yescharacteristic
725C2×C3C3×#101011yescharacteristic
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22#3830⋊C312yes—
732C22C23×(C3⋊D3)⋊C311yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—92no—
739C4—181no—
740C4—181no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—181no—
745C4—181no—
746C3—31no—
747C3—31no—
748C3—61no—
749C3C3×#565011yescharacteristic
750C2—22no—
751C2—41no—
752C2C2×#3830⋊C311yescharacteristic
753C2#41×(C3⋊D3)⋊C311yescharacteristic
754C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
prime radicalC2×D4×H(3,𝔽3)C22
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #64135⋊C3C2semidirect
5. C2×#3750⋊C3C2semidirect
6. #64099⋊C3C2semidirect
7. #64098⋊C3C2semidirect
8. #64098⋊C3C2semidirect
9. #64096⋊C3C2semidirect
10. #64088⋊C3C2semidirect
11. #64088⋊C3C2semidirect
12. #64087⋊C3C2semidirect
13. #64087⋊C3C2semidirect
14. #64086⋊C3C2semidirect
15. #64086⋊C3C2semidirect
16. #10596121C3semidirect
58. #64135C2×C3semidirect
59. C2×#3750C2×C3semidirect
60. #64099C2×C3semidirect
61. #64098C2×C3semidirect
62. #64098C2×C3semidirect
63. #64096C2×C3semidirect
64. #64088C2×C3semidirect
65. #64088C2×C3semidirect
66. #64087C2×C3semidirect
67. #64087C2×C3semidirect
68. #64086C2×C3semidirect
69. #64086C2×C3semidirect
487. H(3,𝔽3)#552semidirect
683. C32#5650semidirect
684. 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)×#1232
#64144⋊C32
D4×(C3⋊Dic3)⋊C32
#64135⋊C32
C2×#3750⋊C32
#64099⋊C32
#64098⋊C32
#64096⋊C32
#64088⋊C32
#64087⋊C32
#64086⋊C32
#105961213
C3×#56503