Finite Group Databasebeta

← #10596164⋊C3 #13153184

Subgroups — #10596164⋊C3 #13153184

Order 1728.

805 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#125C211yesmaximal, characteristic, complemented
2#64107⋊C3C211yesmaximal, characteristic, complemented
3#64107⋊C3C211yesmaximal, characteristic, complemented
4#64105⋊C3C211yesmaximal, characteristic, complemented
5#64105⋊C3C211yesmaximal, characteristic, complemented
6#64103⋊C3C211yesmaximal, characteristic
7#64103⋊C3C211yesmaximal, characteristic
8#64102⋊C3C211yesmaximal, characteristic
9#64101⋊C3C211yesmaximal, characteristic, complemented
10C4⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
11#64098⋊C3C211yesmaximal, characteristic, complemented
12#64098⋊C3C211yesmaximal, characteristic, complemented
13#64096⋊C3C211yesmaximal, characteristic, complemented
14#64081⋊C3C211yesmaximal, characteristic, complemented
15#64081⋊C3C211yesmaximal, characteristic, complemented
16#10596164C311yesmaximal, characteristic, complemented
17C3×#5693—31nomaximal
18C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic
24C4⋊C4×H(3,𝔽3)C2211yescharacteristic
25C4⋊C4×H(3,𝔽3)C2211yescharacteristic
26C4⋊C4×H(3,𝔽3)C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C4⋊C4×H(3,𝔽3)C2211yescharacteristic
30C42×H(3,𝔽3)C2211yescharacteristic
31#3752⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
41#3750⋊C3C2211yescharacteristic
42#3750⋊C3C2211yescharacteristic
43#3750⋊C3C2211yescharacteristic
44#3750⋊C3C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
50C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#125—21no—
54C32×#125D311yescharacteristic, complemented
55C32×#125C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic, complemented
57#64107C2×C311yescharacteristic, complemented
58#64105C2×C311yescharacteristic, complemented
59#64105C2×C311yescharacteristic, complemented
60#64103C2×C311yescharacteristic
61#64103C2×C311yescharacteristic
62#64102C2×C311yescharacteristic
63#64101C2×C311yescharacteristic, complemented
64C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
65#64098C2×C311yescharacteristic, complemented
66#64098C2×C311yescharacteristic, complemented
67#64096C2×C311yescharacteristic, complemented
68#64081C2×C311yescharacteristic, complemented
69#64081C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#898—31no—
72C3×#896—31no—
73C3×#896—31no—
74C3×#894—31no—
75C3×#894—31no—
76C3×#893—31no—
77C3×#892—31no—
78C3×D3×C4⋊C4—31no—
79C3×#889—31no—
80C3×#889—31no—
81C3×#887—31no—
82C3×#872—31no—
83C3×#872—31no—
84C22×(C3⋊D3)⋊C3C2311yescharacteristic
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
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
94C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
95C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C4⋊((C3⋊D3)⋊C3)—22no—
100C4×(C3⋊D3)⋊C3—22no—
101C4×(C3⋊D3)⋊C3—22no—
102C4×(C3⋊D3)⋊C3—22no—
103C4×(C3⋊D3)⋊C3—22no—
104#634⋊C3—22no—
105C3×#552—91no—
106#5693—31no—
107#5693—91no—
108C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
109C2×C4×C3⋊D3C22×C311yescharacteristic
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×C4×C3⋊D3C22×C311yescharacteristic
112C2×C4×C3⋊D3C22×C311yescharacteristic
113C2×#634C22×C311yescharacteristic
114C2×C3×D12—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×C3×Dic6—31no—
120C32×C4⋊C4—21no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4—21no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C4⋊C4C2×D311yescharacteristic
128C32×C4⋊C4C2×D311yescharacteristic
129C32×C4⋊C4C2×D311yescharacteristic
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C4⋊C4C22×C311yescharacteristic
133C32×C4⋊C4C22×C311yescharacteristic
134C32×C4⋊C4C22×C311yescharacteristic
135C32×C4⋊C4C22×C311yescharacteristic
136C32×C4⋊C4C22×C311yescharacteristic
137C32×C4⋊C4C22×C311yescharacteristic
138C32×C42—21no—
139C32×C42C2×D311yescharacteristic
140C32×C42C22×C311yescharacteristic
141#3752C22×C311yescharacteristic
142#3752C22×C311yescharacteristic
143#3752C22×C311yescharacteristic
144#3752C22×C311yescharacteristic
145#3752C22×C311yescharacteristic
146#3752C22×C311yescharacteristic
147#3752C22×C311yescharacteristic
148#3752C22×C311yescharacteristic
149C4⋊(C3⋊Dic3)C22×C311yescharacteristic
150C4⋊(C3⋊Dic3)C22×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
162C4×C3⋊Dic3C22×C311yescharacteristic
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×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×C4⋊Dic3—31no—
172C3×C4⋊Dic3—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×C4×Dic3—31no—
182C3×C4×Dic3—31no—
183C3×C4×Dic3—31no—
184C3×C4×Dic3—31no—
185C22×H(3,𝔽3)C2411yescharacteristic
186C2×(C3⋊D3)⋊C3—21no—
187C2×(C3⋊D3)⋊C3—21no—
188C2×(C3⋊D3)⋊C3—21no—
189C2×(C3⋊D3)⋊C3—21no—
190C2×(C3⋊D3)⋊C3—21no—
191C2×(C3⋊D3)⋊C3#4112yes—
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—
198C4×H(3,𝔽3)—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—31no—
208C3×#125—31no—
209C3×#125—61no—
210C3×#125—91no—
211C3×#125—91no—
212C3×#125C3×D311yescharacteristic
213C3×#123—91no—
214C3×#123—91no—
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#898—31no—
224#898—31no—
225#898—91no—
226#898—91no—
227#896—31no—
228#896—31no—
229#896—91no—
230#896—91no—
231#894—31no—
232#894—31no—
233#894—91no—
234#894—91no—
235#893—31no—
236#893—91no—
237#892—31no—
238#892—91no—
239D3×C4⋊C4—31no—
240D3×C4⋊C4—91no—
241#889—31no—
242#889—31no—
243#889—91no—
244#889—91no—
245#887—31no—
246#887—91no—
247#872—31no—
248#872—31no—
249#872—91no—
250#872—91no—
251C22×C3⋊D3C23×C311yescharacteristic
252C22×C3⋊D3C23×C311yescharacteristic
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C2×C32×C4—21no—
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×C4C22×D311yescharacteristic
269C2×C32×C4C23×C311yescharacteristic
270C2×C32×C4C23×C311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272C2×C32×C4C23×C311yescharacteristic
273C2×C32×C4C23×C311yescharacteristic
274C2×C32×C4C23×C311yescharacteristic
275C2×C32×C4C23×C311yescharacteristic
276C2×C3⋊Dic3C23×C311yescharacteristic
277C2×C3⋊Dic3C23×C311yescharacteristic
278C2×C3⋊Dic3C23×C311yescharacteristic
279C2×C3⋊Dic3C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C311yescharacteristic
281C2×C3⋊Dic3C23×C311yescharacteristic
282C4⋊(C3⋊D3)—22no—
283C4×C3⋊D3—22no—
284C4×C3⋊D3—22no—
285C4×C3⋊D3—22no—
286C4×C3⋊D3—22no—
287#634—22no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C3×D12—62no—
295C3×C4×D3—62no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×Dic6—62no—
300#552—91noSylow
301C2×H(3,𝔽3)C2×#4111yescharacteristic
302C2×H(3,𝔽3)C2×#4111yescharacteristic
303C2×H(3,𝔽3)2−1+411yescharacteristic
304(C3⋊D3)⋊C3—22no—
305(C3⋊D3)⋊C3—41no—
306C2×C3×Q8—91no—
307C2×C3×D4—91no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C22×C3×C4—91no—
312C2×D12—31no—
313C2×D12—91no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×Dic6—31no—
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—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
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⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C4⋊C4—91no—
352C3×C4⋊C4C2×C3×D311yescharacteristic
353C3×C4⋊C4C2×C3×D311yescharacteristic
354C3×C4⋊C4C2×C3×D311yescharacteristic
355C3×C4⋊C4C2×C3×D311yescharacteristic
356C3×C4⋊C4C2×C3×D311yescharacteristic
357C3×C4⋊C4C2×C3×D311yescharacteristic
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4—91no—
366C3×C42—31no—
367C3×C42—31no—
368C3×C42—61no—
369C3×C42—91no—
370C3×C42—91no—
371C3×C42—91no—
372C3×C42—91no—
373C3×C42C2×C3×D311yescharacteristic
374(C2×D3)⋊C4—31no—
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—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—91no—
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—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
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—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—91no—
418C22×C32—21no—
419C22×C32C23×D311yescharacteristic
420C22×C32C24×C311yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3C3×#4112yes—
427C2×C3×D3—32no—
428C2×C3×D3—61no—
429C2×C3×D3—61no—
430C2×C3×D3—61no—
431C2×C3×D3—61no—
432C2×C3×D3—61no—
433C32×C4—22no—
434C32×C4—21no—
435C32×C4—21no—
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×Dic3—32no—
461C3×Dic3—61no—
462C3×Dic3—61no—
463C3×Dic3—61no—
464C3×Dic3—61no—
465C3×Dic3—61no—
466#126—91no—
467#126—91no—
468#125—91no—
469#125—91no—
470#125(C3⋊D3)⋊C311yescharacteristic, complemented
471#123—91no—
472#123—91no—
473C22⋊Q8—91no—
474C22⋊Q8—91no—
475C4×Q8—91no—
476C4×D4—91no—
477#117—91no—
478#117—91no—
479#117—91no—
480C2×C4⋊C4—91no—
481H(3,𝔽3)#55211yescharacteristic, complemented, Sylow
482C23×C3—91no—
483C23×C3—91no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—91no—
487C22×D3—91no—
488C3×Q8—182no—
489C3×D4—182no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
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—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—91no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4—182no—
519C2×C3×C4—182no—
520C2×C3×C4—182no—
521C2×C3×C4C22×C3×D311yescharacteristic
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
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540D12—62no—
541D12—182no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—62no—
545C4×D3—62no—
546C4×D3—182no—
547C4×D3—182no—
548C4×D3—182no—
549C4×D3—182no—
550Dic6—62no—
551Dic6—182no—
552C2×C32—21no—
553C2×C32—21no—
554C2×C32—21no—
555C2×C32#100711yescharacteristic
556C2×C32D3×#4111yescharacteristic
557C2×C32D3×#4111yescharacteristic
558C2×C32C2×C3×#4111yescharacteristic
559C2×C32C2×C3×#4111yescharacteristic
560C2×C32C3×2−1+411yescharacteristic
561C3⋊D3—22no—
562C3⋊D3—41no—
563C3×D3—62no—
564C3×D3—121no—
565C2×Q8—91no—
566C2×D4—91no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
582C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
583C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
584C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
585C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
586C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C42—91no—
596C42—91no—
597C42—91no—
598C42—91no—
599C42C2×(C3⋊D3)⋊C311yescharacteristic
600C22×C3—31no—
601C22×C3—31no—
602C22×C3—61no—
603C22×C3—92no—
604C22×C3—181no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3C23×C3×D311yescharacteristic
610C2×D3—32no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—92no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—181no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—61no—
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—62no—
644C3×C4—92no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656Dic3—32no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—92no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668C32—21no—
669C32#569311yescharacteristic, complemented
670C32C3×#55211yescharacteristic, complemented
671C23—91no—
672C23—91no—
673Q8—182no—
674D4—182no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—91no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—91no—
681C2×C4—182no—
682C2×C4—182no—
683C2×C4—182no—
684C2×C4—182no—
685C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
686C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
687C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
688C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
689C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
690C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
691C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
692C2×C3—31no—
693C2×C3—31no—
694C2×C3—31no—
695C2×C3—31no—
696C2×C3—31no—
697C2×C3—31no—
698C2×C3—61no—
699C2×C3—61no—
700C2×C3—61no—
701C2×C3—182no—
702C2×C3—361no—
703C2×C3C3×#100711yescharacteristic
704C2×C3C3×D3×#4111yescharacteristic
705C2×C3C3×D3×#4111yescharacteristic
706D3—62no—
707D3—121no—
708D3—182no—
709D3—361no—
710C22—92no—
711C22—181no—
712C22—181no—
713C22—181no—
714C22—181no—
715C22—181no—
716C22C23×(C3⋊D3)⋊C311yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—21no—
724C4—92no—
725C4—181no—
726C4—181no—
727C4—181no—
728C4—181no—
729C4—181no—
730C3—31no—
731C3—31no—
732C3—61no—
733C3C3×#569311yescharacteristic
734C2—182no—
735C2—361no—
736C2#1172262711yescharacteristic
737C2#41×(C3⋊D3)⋊C311yescharacteristic
738C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#125C2
prime radicalC2×C4⋊((C3⋊D3)⋊C3)C22
hypercenter#125(C3⋊D3)⋊C3
hypocenterC32C3×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#125C2semidirect
2. #64107⋊C3C2semidirect
3. #64107⋊C3C2semidirect
4. #64105⋊C3C2semidirect
5. #64105⋊C3C2semidirect
9. #64101⋊C3C2semidirect
10. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
11. #64098⋊C3C2semidirect
12. #64098⋊C3C2semidirect
13. #64096⋊C3C2semidirect
14. #64081⋊C3C2semidirect
15. #64081⋊C3C2semidirect
16. #10596164C3semidirect
54. C32×#125D3semidirect
55. C32×#125C2×C3semidirect
56. #64107C2×C3semidirect
57. #64107C2×C3semidirect
58. #64105C2×C3semidirect
59. #64105C2×C3semidirect
63. #64101C2×C3semidirect
64. C4⋊C4×C3⋊D3C2×C3semidirect
65. #64098C2×C3semidirect
66. #64098C2×C3semidirect
67. #64096C2×C3semidirect
68. #64081C2×C3semidirect
69. #64081C2×C3semidirect
470. #125(C3⋊D3)⋊C3semidirect
481. H(3,𝔽3)#552semidirect
669. C32#5693semidirect
670. 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)×#1252
#64107⋊C32
#64105⋊C32
#64103⋊C32
#64102⋊C32
#64101⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64098⋊C32
#64096⋊C32
#64081⋊C32
#105961643
C3×#56933