Finite Group Databasebeta

← #10596173⋊C3 #13153232

Subgroups — #10596173⋊C3 #13153232

Order 1728.

802 conjugacy classes of subgroups.

The subgroup lattice has 746 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#64107⋊C3C211yesmaximal, characteristic, complemented
4#64105⋊C3C211yesmaximal, characteristic, complemented
5#64097⋊C3C211yesmaximal, characteristic, complemented
6#64096⋊C3C211yesmaximal, characteristic, complemented
7#64096⋊C3C211yesmaximal, characteristic, complemented
8#64094⋊C3C211yesmaximal, characteristic
9#64094⋊C3C211yesmaximal, characteristic
10#64090⋊C3C211yesmaximal, characteristic
11#64088⋊C3C211yesmaximal, characteristic, complemented
12#64087⋊C3C211yesmaximal, characteristic, complemented
13#64086⋊C3C211yesmaximal, characteristic, complemented
14#64081⋊C3C211yesmaximal, characteristic, complemented
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10596173C311yesmaximal, characteristic, complemented
17C3×#5702—31nomaximal
18C2×#638⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×#634⋊C3C2211yescharacteristic
22C2×#634⋊C3C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C22⋊C4×H(3,𝔽3)C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29C22⋊C4×H(3,𝔽3)C2211yescharacteristic
30C42×H(3,𝔽3)C2211yescharacteristic
31#3757⋊C3C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
39C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
40#3750⋊C3C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
49C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#126—21no—
54C32×#126D311yescharacteristic, complemented
55C32×#126C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic, complemented
57#64107C2×C311yescharacteristic, complemented
58#64105C2×C311yescharacteristic, complemented
59#64097C2×C311yescharacteristic, complemented
60#64096C2×C311yescharacteristic, complemented
61#64096C2×C311yescharacteristic, complemented
62#64094C2×C311yescharacteristic
63#64094C2×C311yescharacteristic
64#64090C2×C311yescharacteristic
65#64088C2×C311yescharacteristic, complemented
66#64087C2×C311yescharacteristic, complemented
67#64086C2×C311yescharacteristic, complemented
68#64081C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#898—31no—
72C3×#896—31no—
73C3×#888—31no—
74C3×#887—31no—
75C3×#887—31no—
76C3×#885—31no—
77C3×#885—31no—
78C3×#67⋊C4—31no—
79C3×#879—31no—
80C3×#878—31no—
81C3×#877—31no—
82C3×#872—31no—
83C3×C4×Dic6—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C2×C4×H(3,𝔽3)C2311yescharacteristic
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
92#638⋊C3—22no—
93C2×(C3⋊Dic3)⋊C3—22no—
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C4×(C3⋊D3)⋊C3—22no—
102#634⋊C3—22no—
103#634⋊C3—22no—
104#634⋊C3—22no—
105C3×#556—91no—
106#5702—31no—
107#5702—91no—
108C2×#638C22×C311yescharacteristic
109C22×C3⋊Dic3C22×C311yescharacteristic
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×#634C22×C311yescharacteristic
112C2×#634C22×C311yescharacteristic
113C2×#634C22×C311yescharacteristic
114C2×C3×#67—31no—
115C22×C3×Dic3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—31no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C22×C311yescharacteristic
127C32×C4⋊C4C22×C311yescharacteristic
128C32×C4⋊C4C22×C311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C22⋊C4—21no—
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C22⋊C4C2×D311yescharacteristic
135C32×C22⋊C4C22×C311yescharacteristic
136C32×C22⋊C4C22×C311yescharacteristic
137C32×C22⋊C4C22×C311yescharacteristic
138C32×C42—21no—
139C32×C42C2×D311yescharacteristic
140C32×C42C22×C311yescharacteristic
141#3757C22×C311yescharacteristic
142#3757C22×C311yescharacteristic
143#3752C22×C311yescharacteristic
144#3752C22×C311yescharacteristic
145#3752C22×C311yescharacteristic
146#3752C22×C311yescharacteristic
147#3752C22×C311yescharacteristic
148C4⋊(C3⋊Dic3)C22×C311yescharacteristic
149C4⋊(C3⋊Dic3)C22×C311yescharacteristic
150#3750C22×C311yescharacteristic
151#3750C22×C311yescharacteristic
152#3750C22×C311yescharacteristic
153#3750C22×C311yescharacteristic
154#3750C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156#3750C22×C311yescharacteristic
157C4×C3⋊Dic3C22×C311yescharacteristic
158C4×C3⋊Dic3C22×C311yescharacteristic
159C4×C3⋊Dic3C22×C311yescharacteristic
160C4×C3⋊Dic3C22×C311yescharacteristic
161C4×C3⋊Dic3C22×C311yescharacteristic
162C4×C3⋊Dic3C22×C311yescharacteristic
163C3×#217—31no—
164C3×#217—31no—
165C3×(C2×D3)⋊C4—31no—
166C3×(C2×D3)⋊C4—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—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×C4×Dic3—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)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#4112yes—
204(C3⋊Dic3)⋊C3#4112yes—
205C3×C4⋊Q8—91no—
206C3×#126—31no—
207C3×#126—31no—
208C3×#126—61no—
209C3×#126—91no—
210C3×#126—91no—
211C3×#126—91no—
212C3×#126C3×D311yescharacteristic
213C3×#124—91no—
214C3×#124—91no—
215C3×C22⋊Q8—91no—
216C3×C22⋊Q8—91no—
217C3×C4×Q8—91no—
218C3×C4×Q8—91no—
219C3×C4×Q8—91no—
220C3×C4×D4—91no—
221C3×#117—91no—
222C3×#117—91no—
223#898—31no—
224#898—31no—
225#898—91no—
226#898—91no—
227#896—31no—
228#896—91no—
229#888—31no—
230#888—91no—
231#887—31no—
232#887—31no—
233#887—91no—
234#887—91no—
235#885—31no—
236#885—31no—
237#885—91no—
238#885—91no—
239#67⋊C4—31no—
240#67⋊C4—91no—
241#879—31no—
242#879—91no—
243#878—31no—
244#878—91no—
245#877—31no—
246#877—91no—
247#872—31no—
248#872—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—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C23×C311yescharacteristic
269C2×C32×C4C23×C311yescharacteristic
270C2×C32×C4C23×C311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272C2×C32×C4C23×C311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274#638—22no—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3C23×C311yescharacteristic
277C2×C3⋊Dic3C23×C311yescharacteristic
278C2×C3⋊Dic3C23×C311yescharacteristic
279C2×C3⋊Dic3C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C311yescharacteristic
281C2×C3⋊Dic3C23×C311yescharacteristic
282C2×C3⋊Dic3C23×C311yescharacteristic
283C4×C3⋊D3—22no—
284#634—22no—
285#634—22no—
286#634—22no—
287C3×#67—62no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—62no—
296C3×C4×D3—62no—
297C3×Dic6—62no—
298C3×Dic6—62no—
299C3×Dic6—62no—
300#556—91noSylow
301C2×H(3,𝔽3)—41no—
302C2×H(3,𝔽3)C2×#4111yescharacteristic
303C2×H(3,𝔽3)C2×#4111yescharacteristic
304C2×H(3,𝔽3)2−1+411yescharacteristic
305(C3⋊D3)⋊C3—41no—
306C2×C3×Q8—91no—
307C2×C3×Q8—91no—
308C2×C3×Q8—91no—
309C2×C3×D4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C2×#67—31no—
313C2×#67—91no—
314C22×Dic3—31no—
315C22×Dic3—91no—
316C2×C4×D3—31no—
317C2×C4×D3—91no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—91no—
322C2×Dic6—91no—
323C2×Dic6—91no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
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—61no—
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⋊C4C2×C3×D311yescharacteristic
343C3×C4⋊C4C2×C3×D311yescharacteristic
344C3×C4⋊C4C2×C3×D311yescharacteristic
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
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⋊C4—91no—
361C3×C22⋊C4C2×C3×D311yescharacteristic
362C3×C22⋊C4C2×C3×D311yescharacteristic
363C3×C22⋊C4C2×C3×D311yescharacteristic
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—91no—
368C3×C42—91no—
369C3×C42—91no—
370C3×C42—91no—
371C3×C42—91no—
372C3×C42—91no—
373C3×C42C2×C3×D311yescharacteristic
374#217—31no—
375#217—31no—
376#217—91no—
377#217—91no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—91no—
391C4⋊Dic3—91no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—31no—
398Dic3⋊C4—31no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C23×D311yescharacteristic
429C22×C32C24×C311yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3×D3—61no—
434C2×C3×D3—61no—
435C2×C3×D3—61no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—21no—
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—41no—
449C32×C4—41no—
450C32×C4—41no—
451C32×C4—41no—
452C32×C4—41no—
453C32×C4—41no—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—21no—
459C3⋊Dic3C3×#4112yes—
460C3⋊Dic3C3×#4112yes—
461C3×Dic3—32no—
462C3×Dic3—32no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466C3×Dic3—61no—
467C3×Dic3—61no—
468C4⋊Q8—91no—
469#126—91no—
470#126—91no—
471#126—91no—
472#126(C3⋊D3)⋊C311yescharacteristic, complemented
473#124—91no—
474#124—91no—
475C22⋊Q8—91no—
476C22⋊Q8—91no—
477C4×Q8—91no—
478C4×Q8—91no—
479C4×Q8—91no—
480C4×D4—91no—
481#117—91no—
482#117—91no—
483H(3,𝔽3)#55611yescharacteristic, complemented, Sylow
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—61no—
487C23×C3—91no—
488C23×C3C22×C3×D311yescharacteristic
489C22×D3—31no—
490C22×D3—91no—
491C3×Q8—182no—
492C3×Q8—182no—
493C3×Q8—182no—
494C3×D4—182no—
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—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—182no—
521C2×C3×C4—182no—
522C2×C3×C4C22×C3×D311yescharacteristic
523C2×C3×C4C22×C3×D311yescharacteristic
524C2×C3×C4C22×C3×D311yescharacteristic
525C2×C3×C4C22×C3×D311yescharacteristic
526C2×C3×C4C22×C3×D311yescharacteristic
527C2×C3×C4C22×C3×D311yescharacteristic
528#67—62no—
529#67—182no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—62no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—91no—
544C2×Dic3—91no—
545C2×Dic3—182no—
546C4×D3—62no—
547C4×D3—182no—
548Dic6—62no—
549Dic6—62no—
550Dic6—62no—
551Dic6—182no—
552Dic6—182no—
553Dic6—182no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—21no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32—81no—
560C2×C32D3×#4111yescharacteristic
561C2×C32D3×#4111yescharacteristic
562C2×C32#101011yescharacteristic
563C2×C32C2×C3×#4111yescharacteristic
564C2×C32C2×C3×#4111yescharacteristic
565C2×C32C3×2−1+411yescharacteristic
566C3⋊D3—41no—
567C3×D3—121no—
568C2×Q8—91no—
569C2×Q8—91no—
570C2×Q8—91no—
571C2×D4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
584C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
585C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
594C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
595C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
596C42—91no—
597C42—91no—
598C42—91no—
599C42—91no—
600C42—91no—
601C42—91no—
602C42C2×(C3⋊D3)⋊C311yescharacteristic
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—31no—
607C22×C3—31no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3C23×C3×D311yescharacteristic
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—181no—
626C2×D3—181no—
627C2×D3—181no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—61no—
635C3×C4—61no—
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—92no—
647C3×C4—92no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4—181no—
658C3×C4—181no—
659Dic3—32no—
660Dic3—32no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—92no—
667Dic3—92no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673C32—21no—
674C32#570211yescharacteristic, complemented
675C32C3×#55611yescharacteristic, complemented
676C23—91no—
677C23C22×(C3⋊D3)⋊C311yescharacteristic
678Q8—182no—
679Q8—182no—
680Q8—182no—
681D4—182no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—182no—
690C2×C4—182no—
691C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
692C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
693C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
694C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
695C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
696C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
697C2×C3—31no—
698C2×C3—31no—
699C2×C3—31no—
700C2×C3—31no—
701C2×C3—31no—
702C2×C3—31no—
703C2×C3—41no—
704C2×C3—61no—
705C2×C3—61no—
706C2×C3—61no—
707C2×C3—121no—
708C2×C3—121no—
709C2×C3—241no—
710C2×C3—361no—
711C2×C3C3×D3×#4111yescharacteristic
712C2×C3C3×D3×#4111yescharacteristic
713C2×C3C3×#101011yescharacteristic
714D3—121no—
715D3—361no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—181no—
720C22—181no—
721C22—181no—
722C22C23×(C3⋊D3)⋊C311yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—92no—
730C4—92no—
731C4—181no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—181no—
736C3—31no—
737C3—31no—
738C3—61no—
739C3C3×#570211yescharacteristic
740C2—41no—
741C2—361no—
742C2#41×(C3⋊D3)⋊C311yescharacteristic
743C2#41×(C3⋊D3)⋊C311yescharacteristic
744C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#126C2
prime radicalC2×#638⋊C3C22
hypercenter#126(C3⋊D3)⋊C3
hypocenterC32C3×#556
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. #64107⋊C3C2semidirect
4. #64105⋊C3C2semidirect
5. #64097⋊C3C2semidirect
6. #64096⋊C3C2semidirect
7. #64096⋊C3C2semidirect
11. #64088⋊C3C2semidirect
12. #64087⋊C3C2semidirect
13. #64086⋊C3C2semidirect
14. #64081⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10596173C3semidirect
54. C32×#126D3semidirect
55. C32×#126C2×C3semidirect
56. #64107C2×C3semidirect
57. #64107C2×C3semidirect
58. #64105C2×C3semidirect
59. #64097C2×C3semidirect
60. #64096C2×C3semidirect
61. #64096C2×C3semidirect
65. #64088C2×C3semidirect
66. #64087C2×C3semidirect
67. #64086C2×C3semidirect
68. #64081C2×C3semidirect
69. C4×#634C2×C3semidirect
472. #126(C3⋊D3)⋊C3semidirect
483. H(3,𝔽3)#556semidirect
674. C32#5702semidirect
675. C32C3×#556semidirect

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
#64105⋊C32
#64097⋊C32
#64096⋊C32
#64094⋊C32
#64090⋊C32
#64088⋊C32
#64087⋊C32
#64086⋊C32
#64081⋊C32
C4×#634⋊C32
#105961733
C3×#57023