Finite Group Databasebeta

← #10595999⋊C3 #13152522

Subgroups — #10595999⋊C3 #13152522

Order 1728.

895 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#117C211yesmaximal, characteristic, complemented
2C4×#638⋊C3C211yesmaximal, characteristic, complemented
3C4×#638⋊C3C211yesmaximal, characteristic, complemented
4#64107⋊C3C211yesmaximal, characteristic, complemented
5#64105⋊C3C211yesmaximal, characteristic, complemented
6#64103⋊C3C211yesmaximal, characteristic, complemented
7#64098⋊C3C211yesmaximal, characteristic, complemented
8#64094⋊C3C211yesmaximal, characteristic, complemented
9#64093⋊C3C211yesmaximal, characteristic
10#64092⋊C3C211yesmaximal, characteristic, complemented
11#64088⋊C3C211yesmaximal, characteristic, complemented
12C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
13#64081⋊C3C211yesmaximal, characteristic, complemented
14C42×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
15C4×#634⋊C3C211yesmaximal, characteristic, complemented
16#10595999C311yesmaximal, characteristic, complemented
17C3×#5528—31nomaximal
18C22×C4×H(3,𝔽3)C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C22⋊C4×H(3,𝔽3)C2211yescharacteristic
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C42×H(3,𝔽3)C2211yescharacteristic
32C42×H(3,𝔽3)C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
42C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
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×#117—21no—
54C32×#117D311yescharacteristic, complemented
55C32×#117C2×C311yescharacteristic, complemented
56C4×#638C2×C311yescharacteristic, complemented
57C4×#638C2×C311yescharacteristic, complemented
58#64107C2×C311yescharacteristic, complemented
59#64105C2×C311yescharacteristic, complemented
60#64103C2×C311yescharacteristic, complemented
61#64098C2×C311yescharacteristic, complemented
62#64094C2×C311yescharacteristic, complemented
63#64093C2×C311yescharacteristic
64#64092C2×C311yescharacteristic, complemented
65#64088C2×C311yescharacteristic, complemented
66C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
67#64081C2×C311yescharacteristic, complemented
68C42×C3⋊D3C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×C4×#67—31no—
71C3×C4×#67—31no—
72C3×#898—31no—
73C3×#896—31no—
74C3×#894—31no—
75C3×#889—31no—
76C3×#885—31no—
77C3×#884—31no—
78C3×#883—31no—
79C3×#879—31no—
80C3×C4×D12—31no—
81C3×#872—31no—
82C3×C42×D3—31no—
83C3×C4×Dic6—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
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×C4×H(3,𝔽3)C2311yescharacteristic
94#638⋊C3—22no—
95#638⋊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
102C4⋊((C3⋊D3)⋊C3)—22no—
103C4×(C3⋊D3)⋊C3—22no—
104C4×(C3⋊D3)⋊C3—22no—
105C4×(C3⋊D3)⋊C3—22no—
106C4×(C3⋊D3)⋊C3—22no—
107#634⋊C3—22no—
108C3×#529—91no—
109#5528—31no—
110#5528—91no—
111C22×C32×C4—21no—
112C22×C32×C4C2×D311yescharacteristic
113C22×C32×C4C22×C311yescharacteristic
114C2×#638C22×C311yescharacteristic
115C2×#638C22×C311yescharacteristic
116C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
117C2×C4×C3⋊D3C22×C311yescharacteristic
118C2×C4×C3⋊D3C22×C311yescharacteristic
119C2×C4×C3⋊D3C22×C311yescharacteristic
120C2×C4×C3⋊D3C22×C311yescharacteristic
121C2×#634C22×C311yescharacteristic
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×D12—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×Dic6—31no—
130C32×C4⋊C4—21no—
131C32×C4⋊C4—21no—
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C4⋊C4C2×D311yescharacteristic
134C32×C4⋊C4C22×C311yescharacteristic
135C32×C4⋊C4C22×C311yescharacteristic
136C32×C22⋊C4—21no—
137C32×C22⋊C4—21no—
138C32×C22⋊C4C2×D311yescharacteristic
139C32×C22⋊C4C2×D311yescharacteristic
140C32×C22⋊C4C22×C311yescharacteristic
141C32×C22⋊C4C22×C311yescharacteristic
142C32×C42—21no—
143C32×C42—21no—
144C32×C42C2×D311yescharacteristic
145C32×C42C2×D311yescharacteristic
146C32×C42C22×C311yescharacteristic
147C32×C42C22×C311yescharacteristic
148#3757C22×C311yescharacteristic
149#3757C22×C311yescharacteristic
150#3752C22×C311yescharacteristic
151#3752C22×C311yescharacteristic
152#3752C22×C311yescharacteristic
153#3752C22×C311yescharacteristic
154#3752C22×C311yescharacteristic
155#3752C22×C311yescharacteristic
156C4⋊(C3⋊Dic3)C22×C311yescharacteristic
157C4⋊(C3⋊Dic3)C22×C311yescharacteristic
158#3750C22×C311yescharacteristic
159#3750C22×C311yescharacteristic
160#3750C22×C311yescharacteristic
161#3750C22×C311yescharacteristic
162#3750C22×C311yescharacteristic
163#3750C22×C311yescharacteristic
164C4×C3⋊Dic3C22×C311yescharacteristic
165C4×C3⋊Dic3C22×C311yescharacteristic
166C4×C3⋊Dic3C22×C311yescharacteristic
167C4×C3⋊Dic3C22×C311yescharacteristic
168C3×#217—31no—
169C3×#217—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×C4×Dic3—31no—
185C3×C4×Dic3—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—31no—
188C22×H(3,𝔽3)—21no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)C2411yescharacteristic
192C2×(C3⋊D3)⋊C3—21no—
193C2×(C3⋊D3)⋊C3—21no—
194C2×(C3⋊D3)⋊C3—21no—
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3#4112yes—
198C4×H(3,𝔽3)—21no—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)—21no—
201C4×H(3,𝔽3)—21no—
202C4×H(3,𝔽3)—21no—
203C4×H(3,𝔽3)#4112yes—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3#4112yes—
210C3×#126—91no—
211C3×#126—91no—
212C3×#125—91no—
213C3×#124—91no—
214C3×#123—91no—
215C3×#123—91no—
216C3×C22⋊Q8—91no—
217C3×#121—91no—
218C3×C4×Q8—91no—
219C3×C4×D4—91no—
220C3×C4×D4—91no—
221C3×C4×D4—91no—
222C3×#117—31no—
223C3×#117—31no—
224C3×#117—61no—
225C3×#117—91no—
226C3×#117C3×D311yescharacteristic
227C2×C3×C42—91no—
228C4×#67—31no—
229C4×#67—31no—
230C4×#67—91no—
231C4×#67—91no—
232#898—31no—
233#898—91no—
234#896—31no—
235#896—91no—
236#894—31no—
237#894—91no—
238#889—31no—
239#889—91no—
240#885—31no—
241#885—91no—
242#884—31no—
243#884—91no—
244#883—31no—
245#883—91no—
246#879—31no—
247#879—91no—
248C4×D12—31no—
249C4×D12—91no—
250#872—31no—
251#872—91no—
252C42×D3—31no—
253C42×D3—91no—
254C4×Dic6—31no—
255C4×Dic6—91no—
256C23×C32—21no—
257C23×C32C22×D311yescharacteristic
258C23×C32C23×C311yescharacteristic
259C22×C3⋊D3C23×C311yescharacteristic
260C22×C3⋊D3C23×C311yescharacteristic
261C22×C3×D3—31no—
262C22×C3×D3—31no—
263C2×C32×C4—24no—
264C2×C32×C4—22no—
265C2×C32×C4—22no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C311yescharacteristic
279C2×C32×C4C23×C311yescharacteristic
280C2×C32×C4C23×C311yescharacteristic
281C2×C32×C4C23×C311yescharacteristic
282C2×C32×C4C23×C311yescharacteristic
283C2×C32×C4C23×C311yescharacteristic
284#638—22no—
285#638—22no—
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C311yescharacteristic
288C2×C3⋊Dic3C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C311yescharacteristic
290C2×C3⋊Dic3C23×C311yescharacteristic
291C2×C3⋊Dic3C23×C311yescharacteristic
292C4⋊(C3⋊D3)—22no—
293C4×C3⋊D3—22no—
294C4×C3⋊D3—22no—
295C4×C3⋊D3—22no—
296C4×C3⋊D3—22no—
297#634—22no—
298C3×#67—62no—
299C3×#67—62no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C3×D12—62no—
307C3×C4×D3—62no—
308C3×C4×D3—62no—
309C3×C4×D3—62no—
310C3×C4×D3—62no—
311C3×Dic6—62no—
312#529—91noSylow
313C2×H(3,𝔽3)—41no—
314C2×H(3,𝔽3)C2×#4111yescharacteristic
315C2×H(3,𝔽3)C2×#4111yescharacteristic
316C2×H(3,𝔽3)C2×#4111yescharacteristic
317(C3⋊D3)⋊C3—22no—
318(C3⋊D3)⋊C3—41no—
319C2×C3×Q8—91no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C22×C3×C4C2×C3×D311yescharacteristic
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—91no—
334C2×#67—91no—
335C2×D12—31no—
336C2×D12—91no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—31no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—91no—
344C2×C4×D3—91no—
345C2×Dic6—31no—
346C2×Dic6—91no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—91no—
354C3×C4⋊C4—91no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4C2×C3×D311yescharacteristic
362C3×C4⋊C4C2×C3×D311yescharacteristic
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4C2×C3×D311yescharacteristic
378C3×C22⋊C4C2×C3×D311yescharacteristic
379C3×C42—31no—
380C3×C42—31no—
381C3×C42—31no—
382C3×C42—31no—
383C3×C42—61no—
384C3×C42—61no—
385C3×C42—91no—
386C3×C42—91no—
387C3×C42—91no—
388C3×C42—91no—
389C3×C42C2×C3×D311yescharacteristic
390C3×C42C2×C3×D311yescharacteristic
391#217—31no—
392#217—31no—
393#217—91no—
394#217—91no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—91no—
410C4⋊Dic3—91no—
411Dic3⋊C4—31no—
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—31no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—31no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C22×C32—22no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C23×D311yescharacteristic
442C22×C32C24×C311yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3C3×#4112yes—
449C2×C3×D3—32no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C32×C4—22no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—22no—
467C32×C4—41no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4#23512yes—
472C32×C4C3×#4112yes—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3C3×#4112yes—
479C3×Dic3—32no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—61no—
484C3×Dic3—61no—
485#126—91no—
486#126—91no—
487#125—91no—
488#124—91no—
489#123—91no—
490#123—91no—
491C22⋊Q8—91no—
492#121—91no—
493C4×Q8—91no—
494C4×D4—91no—
495C4×D4—91no—
496C4×D4—91no—
497#117—91no—
498#117(C3⋊D3)⋊C311yescharacteristic, complemented
499C2×C42—91no—
500H(3,𝔽3)#52911yescharacteristic, complemented, Sylow
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—61no—
504C23×C3—91no—
505C23×C3—91no—
506C23×C3C22×C3×D311yescharacteristic
507C22×D3—31no—
508C22×D3—31no—
509C22×D3—91no—
510C22×D3—91no—
511C3×Q8—182no—
512C3×D4—182no—
513C3×D4—182no—
514C3×D4—182no—
515C2×C3×C4—22no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—62no—
529C2×C3×C4—62no—
530C2×C3×C4—64no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—182no—
544C2×C3×C4—182no—
545C2×C3×C4—182no—
546C2×C3×C4—182no—
547C2×C3×C4C22×C3×D311yescharacteristic
548C2×C3×C4C22×C3×D311yescharacteristic
549C2×C3×C4C22×C3×D311yescharacteristic
550C2×C3×C4C22×C3×D311yescharacteristic
551C2×C3×C4C22×C3×D311yescharacteristic
552C2×C3×C4C22×C3×D311yescharacteristic
553#67—62no—
554#67—62no—
555#67—182no—
556#67—182no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569D12—62no—
570D12—182no—
571C4×D3—62no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579Dic6—62no—
580Dic6—182no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—42no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32C2×#23511yescharacteristic
588C2×C32D3×#4111yescharacteristic
589C2×C32D3×#4111yescharacteristic
590C2×C32C2×C3×#4111yescharacteristic
591C2×C32C2×C3×#4111yescharacteristic
592C2×C32C2×C3×#4111yescharacteristic
593C3⋊D3—22no—
594C3⋊D3—41no—
595C3×D3—62no—
596C3×D3—121no—
597C2×Q8—91no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—91no—
601C22×C4—91no—
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
615C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
625C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
626C42—91no—
627C42—91no—
628C42—91no—
629C42—91no—
630C42C2×(C3⋊D3)⋊C311yescharacteristic
631C42C2×(C3⋊D3)⋊C311yescharacteristic
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—31no—
636C22×C3—31no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—61no—
645C22×C3—92no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3C23×C3×D311yescharacteristic
654C2×D3—32no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—92no—
661C2×D3—181no—
662C2×D3—181no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—32no—
672C3×C4—32no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—92no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—181no—
691C3×C4—181no—
692C3×C4—181no—
693C3×C4—181no—
694C3×C4—181no—
695C3×C4C3×#23512yes—
696Dic3—32no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—92no—
703Dic3—181no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708C32—21no—
709C32#552811yescharacteristic, complemented
710C32C3×#52911yescharacteristic, complemented
711C23—91no—
712C23—91no—
713C23C22×(C3⋊D3)⋊C311yescharacteristic
714Q8—182no—
715D4—182no—
716D4—182no—
717D4—182no—
718C2×C4—22no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—182no—
726C2×C4—182no—
727C2×C4—182no—
728C2×C4—182no—
729C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
730C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
731C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
732C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
733C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
734C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
735C2×C3—31no—
736C2×C3—31no—
737C2×C3—31no—
738C2×C3—31no—
739C2×C3—31no—
740C2×C3—31no—
741C2×C3—41no—
742C2×C3—61no—
743C2×C3—61no—
744C2×C3—61no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3—122no—
748C2×C3—182no—
749C2×C3—361no—
750C2×C3C2×C3×#23511yescharacteristic
751C2×C3C3×D3×#4111yescharacteristic
752C2×C3C3×D3×#4111yescharacteristic
753D3—62no—
754D3—121no—
755D3—182no—
756D3—361no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—92no—
761C22—181no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22—181no—
766C22C23×(C3⋊D3)⋊C311yescharacteristic
767C4—21no—
768C4—21no—
769C4—21no—
770C4—21no—
771C4—21no—
772C4—92no—
773C4—181no—
774C4—181no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4#3828⋊C312yes—
779C3—31no—
780C3—31no—
781C3—61no—
782C3C3×#552811yescharacteristic
783C2—41no—
784C2—182no—
785C2—361no—
786C2C2×#3828⋊C311yescharacteristic
787C2#41×(C3⋊D3)⋊C311yescharacteristic
788C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2×C4C22×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#117C2
prime radical#64093⋊C3C2
hypercenter#117(C3⋊D3)⋊C3
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#117C2semidirect
2. C4×#638⋊C3C2semidirect
3. C4×#638⋊C3C2semidirect
4. #64107⋊C3C2semidirect
5. #64105⋊C3C2semidirect
6. #64103⋊C3C2semidirect
7. #64098⋊C3C2semidirect
8. #64094⋊C3C2semidirect
10. #64092⋊C3C2semidirect
11. #64088⋊C3C2semidirect
12. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
13. #64081⋊C3C2semidirect
14. C42×(C3⋊D3)⋊C3C2semidirect
15. C4×#634⋊C3C2semidirect
16. #10595999C3semidirect
54. C32×#117D3semidirect
55. C32×#117C2×C3semidirect
56. C4×#638C2×C3semidirect
57. C4×#638C2×C3semidirect
58. #64107C2×C3semidirect
59. #64105C2×C3semidirect
60. #64103C2×C3semidirect
61. #64098C2×C3semidirect
62. #64094C2×C3semidirect
64. #64092C2×C3semidirect
65. #64088C2×C3semidirect
66. C4×C4⋊(C3⋊D3)C2×C3semidirect
67. #64081C2×C3semidirect
68. C42×C3⋊D3C2×C3semidirect
69. C4×#634C2×C3semidirect
498. #117(C3⋊D3)⋊C3semidirect
500. H(3,𝔽3)#529semidirect
709. C32#5528semidirect
710. C32C3×#529semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1172
C4×#638⋊C32
#64107⋊C32
#64105⋊C32
#64103⋊C32
#64098⋊C32
#64094⋊C32
#64093⋊C32
#64092⋊C32
#64088⋊C32
C4×C4⋊((C3⋊D3)⋊C3)2
#64081⋊C32
C42×(C3⋊D3)⋊C32
C4×#634⋊C32
#105959993
C3×#55283