Finite Group Databasebeta

← #10596175⋊C3 #13153235

Subgroups — #10596175⋊C3 #13153235

Order 1728.

935 conjugacy classes of subgroups.

The subgroup lattice has 879 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#64105⋊C3C211yesmaximal, characteristic, complemented
4#64104⋊C3C211yesmaximal, characteristic, complemented
5#64104⋊C3C211yesmaximal, characteristic, complemented
6#64103⋊C3C211yesmaximal, characteristic, complemented
7#64102⋊C3C211yesmaximal, characteristic, complemented
8#64094⋊C3C211yesmaximal, characteristic, complemented
9#64093⋊C3C211yesmaximal, characteristic, complemented
10#64092⋊C3C211yesmaximal, characteristic, complemented
11#64091⋊C3C211yesmaximal, characteristic, complemented
12#64091⋊C3C211yesmaximal, characteristic, complemented
13C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
14#64084⋊C3C211yesmaximal, characteristic, complemented
15C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
16#10596175C311yesmaximal, characteristic, complemented
17C3×#5704—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
30C2×#634⋊C3C2211yescharacteristic, complemented
31C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
32C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
33C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic
36C22⋊C4×H(3,𝔽3)C2211yescharacteristic
37C42×H(3,𝔽3)C2211yescharacteristic, complemented
38#3757⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic
45#3752⋊C3C2211yescharacteristic, complemented
46#3752⋊C3C2211yescharacteristic, complemented
47#3752⋊C3C2211yescharacteristic, complemented
48#3752⋊C3C2211yescharacteristic, complemented
49C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
50#3750⋊C3C2211yescharacteristic, complemented
51#3750⋊C3C2211yescharacteristic, complemented
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
53C32×#126—21no—
54C32×#126D311yescharacteristic, complemented
55C32×#126C2×C311yescharacteristic, complemented
56#64107C2×C311yescharacteristic, complemented
57#64105C2×C311yescharacteristic, complemented
58#64104C2×C311yescharacteristic, complemented
59#64104C2×C311yescharacteristic, complemented
60#64103C2×C311yescharacteristic, complemented
61#64102C2×C311yescharacteristic, complemented
62#64094C2×C311yescharacteristic, complemented
63#64093C2×C311yescharacteristic, complemented
64#64092C2×C311yescharacteristic, complemented
65#64091C2×C311yescharacteristic, complemented
66#64091C2×C311yescharacteristic, complemented
67C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
68#64084C2×C311yescharacteristic, complemented
69C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
70C3×#898—31no—
71C3×#896—31no—
72C3×#895—31no—
73C3×#895—31no—
74C3×#894—31no—
75C3×#893—31no—
76C3×#885—31no—
77C3×#884—31no—
78C3×#883—31no—
79C3×#882—31no—
80C3×#882—31no—
81C3×D3×C22⋊C4—31no—
82C3×#875—31no—
83C3×C4×D12—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3—22no—
86C22×(C3⋊D3)⋊C3—41no—
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97C2×C4×H(3,𝔽3)C2311yescharacteristic
98#638⋊C3—41no—
99#638⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C4⋊((C3⋊D3)⋊C3)—22no—
105C4⋊((C3⋊D3)⋊C3)—22no—
106C4⋊((C3⋊D3)⋊C3)—41no—
107C4⋊((C3⋊D3)⋊C3)—41no—
108C4⋊((C3⋊D3)⋊C3)—41no—
109C4×(C3⋊D3)⋊C3—41no—
110C4×(C3⋊D3)⋊C3—41no—
111C4×(C3⋊D3)⋊C3—41no—
112C4×(C3⋊D3)⋊C3—41no—
113#634⋊C3—41no—
114C3×#538—91no—
115#5704—31no—
116#5704—91no—
117C23×C3⋊D3C22×C311yescharacteristic
118C23×C3×D3—31no—
119C2×#638C22×C311yescharacteristic
120C2×#638C22×C311yescharacteristic
121C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
122C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
123C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
124C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
125C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
126C2×C4×C3⋊D3C22×C311yescharacteristic
127C2×C4×C3⋊D3C22×C311yescharacteristic
128C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
129C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
130C2×#634C22×C311yescharacteristic, complemented
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×D12—31no—
134C2×C3×D12—31no—
135C2×C3×D12—31no—
136C2×C3×D12—31no—
137C2×C3×D12—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×Dic6—31no—
143C32×C4⋊C4—21no—
144C32×C4⋊C4—21no—
145C32×C4⋊C4—21no—
146C32×C4⋊C4C2×D311yescharacteristic, complemented
147C32×C4⋊C4C2×D311yescharacteristic, complemented
148C32×C4⋊C4C2×D311yescharacteristic, complemented
149C32×C4⋊C4C22×C311yescharacteristic, complemented
150C32×C4⋊C4C22×C311yescharacteristic, complemented
151C32×C4⋊C4C22×C311yescharacteristic, complemented
152C32×C22⋊C4—21no—
153C32×C22⋊C4—21no—
154C32×C22⋊C4—21no—
155C32×C22⋊C4C2×D311yescharacteristic
156C32×C22⋊C4C2×D311yescharacteristic
157C32×C22⋊C4C2×D311yescharacteristic
158C32×C22⋊C4C22×C311yescharacteristic
159C32×C22⋊C4C22×C311yescharacteristic
160C32×C22⋊C4C22×C311yescharacteristic
161C32×C42—21no—
162C32×C42C2×D311yescharacteristic, complemented
163C32×C42C22×C311yescharacteristic, complemented
164#3757C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166#3752C22×C311yescharacteristic
167#3752C22×C311yescharacteristic
168#3752C22×C311yescharacteristic
169#3752C22×C311yescharacteristic
170#3752C22×C311yescharacteristic
171#3752C22×C311yescharacteristic, complemented
172#3752C22×C311yescharacteristic, complemented
173#3752C22×C311yescharacteristic, complemented
174#3752C22×C311yescharacteristic, complemented
175C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
176#3750C22×C311yescharacteristic, complemented
177#3750C22×C311yescharacteristic, complemented
178C4×C3⋊Dic3C22×C311yescharacteristic, complemented
179C3×#217—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×C4⋊Dic3—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×C4×Dic3—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C2×(C3⋊D3)⋊C3—21no—
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—44no—
210C2×(C3⋊D3)⋊C3#4112yes—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213C4×H(3,𝔽3)—21no—
214C4×H(3,𝔽3)—21no—
215C4×H(3,𝔽3)—21no—
216C4×H(3,𝔽3)—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221C3×#126—31no—
222C3×#126—31no—
223C3×#126—61no—
224C3×#126—91no—
225C3×#126C3×D311yescharacteristic
226C3×#124—91no—
227C3×#124—91no—
228C3×#123—91no—
229C3×#123—91no—
230C3×C22⋊Q8—91no—
231C3×#121—91no—
232C3×#121—91no—
233C3×#121—91no—
234C3×#120—91no—
235C3×#120—91no—
236C3×C4×D4—91no—
237C3×C4×D4—91no—
238C2×C3×C22⋊C4—91no—
239#898—31no—
240#898—91no—
241#896—31no—
242#896—91no—
243#895—31no—
244#895—31no—
245#895—91no—
246#895—91no—
247#894—31no—
248#894—91no—
249#893—31no—
250#893—91no—
251#885—31no—
252#885—91no—
253#884—31no—
254#884—91no—
255#883—31no—
256#883—91no—
257#882—31no—
258#882—31no—
259#882—91no—
260#882—91no—
261D3×C22⋊C4—31no—
262D3×C22⋊C4—91no—
263#875—31no—
264#875—91no—
265C4×D12—31no—
266C4×D12—91no—
267C23×C32—21no—
268C23×C32C22×D311yescharacteristic
269C23×C32C23×C311yescharacteristic
270C22×C3⋊D3—22no—
271C22×C3⋊D3—41no—
272C22×C3⋊D3—41no—
273C22×C3⋊D3C23×C311yescharacteristic
274C22×C3⋊D3C23×C311yescharacteristic
275C22×C3⋊D3C23×C311yescharacteristic
276C22×C3⋊D3C23×C311yescharacteristic
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—62no—
282C22×C3×D3—121no—
283C22×C3×D3—121no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C23×C311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298C2×C32×C4C23×C311yescharacteristic
299C2×C32×C4C23×C311yescharacteristic
300C2×C32×C4C23×C311yescharacteristic
301C2×C32×C4C23×C311yescharacteristic
302#638—41no—
303#638—41no—
304C2×C3⋊Dic3C23×C311yescharacteristic
305C2×C3⋊Dic3C23×C311yescharacteristic
306C2×C3⋊Dic3C23×C311yescharacteristic
307C2×C3⋊Dic3C23×C311yescharacteristic
308C4⋊(C3⋊D3)—22no—
309C4⋊(C3⋊D3)—22no—
310C4⋊(C3⋊D3)—41no—
311C4⋊(C3⋊D3)—41no—
312C4⋊(C3⋊D3)—41no—
313C4×C3⋊D3—41no—
314C4×C3⋊D3—41no—
315C4×C3⋊D3—41no—
316C4×C3⋊D3—41no—
317#634—41no—
318C3×#67—121no—
319C3×#67—121no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C3×D12—62no—
325C3×D12—62no—
326C3×D12—121no—
327C3×D12—121no—
328C3×D12—121no—
329C3×C4×D3—121no—
330C3×C4×D3—121no—
331C3×C4×D3—121no—
332C3×C4×D3—121no—
333C3×Dic6—121no—
334#538—91noSylow
335C2×H(3,𝔽3)—41no—
336C2×H(3,𝔽3)C2×#4111yescharacteristic
337C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
338C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
339(C3⋊D3)⋊C3—22no—
340(C3⋊D3)⋊C3—41no—
341(C3⋊D3)⋊C3—41no—
342(C3⋊D3)⋊C3—41no—
343C24×C3—91no—
344C23×D3—31no—
345C23×D3—91no—
346C2×C3×Q8—91no—
347C2×C3×D4—91no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C22×C3×C4—91no—
355C22×C3×C4—91no—
356C22×C3×C4—91no—
357C22×C3×C4—91no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—91no—
372C2×C4×D3—31no—
373C2×C4×D3—31no—
374C2×C4×D3—31no—
375C2×C4×D3—31no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×Dic6—31no—
381C2×Dic6—91no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C4⋊C4—91no—
394C3×C4⋊C4C2×C3×D311yescharacteristic
395C3×C4⋊C4C2×C3×D311yescharacteristic
396C3×C4⋊C4C2×C3×D311yescharacteristic
397C3×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4C2×C3×D311yescharacteristic
418C3×C22⋊C4C2×C3×D311yescharacteristic
419C3×C22⋊C4C2×C3×D311yescharacteristic
420C3×C42—31no—
421C3×C42—31no—
422C3×C42—61no—
423C3×C42—91no—
424C3×C42C2×C3×D311yescharacteristic
425#217—31no—
426#217—91no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447C4⋊Dic3—31no—
448C4⋊Dic3—91no—
449Dic3⋊C4—31no—
450Dic3⋊C4—31no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453C4×Dic3—31no—
454C4×Dic3—91no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C23×D311yescharacteristic
466C22×C32C24×C311yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—44no—
479C2×C3⋊D3C3×#4112yes—
480C2×C3×D3—32no—
481C2×C3×D3—61no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—61no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—61no—
489C2×C3×D3—61no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—124no—
493C32×C4—21no—
494C32×C4—21no—
495C32×C4—21no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—21no—
500C32×C4—21no—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—41no—
506C32×C4—41no—
507C32×C4—41no—
508C32×C4—41no—
509C32×C4—41no—
510C32×C4—41no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519#126—91no—
520#126(C3⋊D3)⋊C311yescharacteristic, complemented
521#124—91no—
522#124—91no—
523#123—91no—
524#123—91no—
525C22⋊Q8—91no—
526#121—91no—
527#121—91no—
528#121—91no—
529#120—91no—
530#120—91no—
531C4×D4—91no—
532C4×D4—91no—
533C2×C22⋊C4—91no—
534H(3,𝔽3)#53811yescharacteristic, complemented, Sylow
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—61no—
538C23×C3—91no—
539C23×C3—91no—
540C23×C3—91no—
541C23×C3—91no—
542C23×C3—182no—
543C23×C3—361no—
544C23×C3—361no—
545C23×C3C22×C3×D311yescharacteristic
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—62no—
551C22×D3—91no—
552C22×D3—91no—
553C22×D3—91no—
554C22×D3—91no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—182no—
558C22×D3—361no—
559C22×D3—361no—
560C3×Q8—361no—
561C3×D4—182no—
562C3×D4—182no—
563C3×D4—361no—
564C3×D4—361no—
565C3×D4—361no—
566C3×D4—361no—
567C3×D4—361no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—91no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—361no—
591C2×C3×C4—361no—
592C2×C3×C4—361no—
593C2×C3×C4—361no—
594C2×C3×C4C22×C3×D311yescharacteristic
595C2×C3×C4C22×C3×D311yescharacteristic
596C2×C3×C4C22×C3×D311yescharacteristic
597C2×C3×C4C22×C3×D311yescharacteristic
598C2×C3×C4C22×C3×D311yescharacteristic
599C2×C3×C4C22×C3×D311yescharacteristic
600#67—121no—
601#67—121no—
602#67—361no—
603#67—361no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—91no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—91no—
612D12—62no—
613D12—62no—
614D12—121no—
615D12—121no—
616D12—121no—
617D12—182no—
618D12—182no—
619D12—361no—
620D12—361no—
621D12—361no—
622C4×D3—121no—
623C4×D3—121no—
624C4×D3—121no—
625C4×D3—121no—
626C4×D3—361no—
627C4×D3—361no—
628C4×D3—361no—
629C4×D3—361no—
630Dic6—121no—
631Dic6—361no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—81no—
638C2×C32D3×#4111yescharacteristic
639C2×C32#100911yescharacteristic
640C2×C32#100911yescharacteristic
641C2×C32C2×C3×#4111yescharacteristic
642C2×C32C3×H(5,𝔽2)11yescharacteristic
643C2×C32C3×H(5,𝔽2)11yescharacteristic
644C3⋊D3—22no—
645C3⋊D3—41no—
646C3⋊D3—41no—
647C3⋊D3—41no—
648C3×D3—62no—
649C3×D3—121no—
650C3×D3—121no—
651C3×D3—121no—
652C24—91no—
653C2×Q8—91no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—91no—
661C22×C4—91no—
662C22×C4—91no—
663C22×C4—91no—
664C22×C4—91no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
669C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
670C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
683C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
684C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
685C42—91no—
686C42C2×(C3⋊D3)⋊C311yescharacteristic, complemented
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—31no—
691C22×C3—31no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—92no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—181no—
704C22×C3—181no—
705C22×C3—181no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—181no—
714C22×C3—364no—
715C22×C3C23×C3×D311yescharacteristic
716C2×D3—32no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—92no—
729C2×D3—124no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—181no—
734C2×D3—181no—
735C2×D3—181no—
736C2×D3—181no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3—181no—
741C2×D3—364no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—61no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—121no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—181no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770Dic3—61no—
771Dic3—61no—
772Dic3—61no—
773Dic3—61no—
774Dic3—181no—
775Dic3—181no—
776Dic3—181no—
777Dic3—181no—
778C32—21no—
779C32#570411yescharacteristic, complemented
780C32C3×#53811yescharacteristic, complemented
781C23—91no—
782C23—91no—
783C23—91no—
784C23—91no—
785C23—182no—
786C23—361no—
787C23—361no—
788C23C22×(C3⋊D3)⋊C311yescharacteristic
789Q8—361no—
790D4—182no—
791D4—182no—
792D4—361no—
793D4—361no—
794D4—361no—
795D4—361no—
796D4—361no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—91no—
800C2×C4—91no—
801C2×C4—361no—
802C2×C4—361no—
803C2×C4—361no—
804C2×C4—361no—
805C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
806C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
807C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
808C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
809C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
810C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
811C2×C3—31no—
812C2×C3—31no—
813C2×C3—31no—
814C2×C3—31no—
815C2×C3—31no—
816C2×C3—31no—
817C2×C3—41no—
818C2×C3—61no—
819C2×C3—61no—
820C2×C3—61no—
821C2×C3—121no—
822C2×C3—121no—
823C2×C3—182no—
824C2×C3—241no—
825C2×C3—361no—
826C2×C3—361no—
827C2×C3—361no—
828C2×C3C3×D3×#4111yescharacteristic
829C2×C3C3×#100911yescharacteristic
830C2×C3C3×#100911yescharacteristic
831D3—62no—
832D3—121no—
833D3—121no—
834D3—121no—
835D3—182no—
836D3—361no—
837D3—361no—
838D3—361no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—92no—
843C22—181no—
844C22—181no—
845C22—181no—
846C22—181no—
847C22—181no—
848C22—181no—
849C22—181no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—364no—
855C22C23×(C3⋊D3)⋊C311yescharacteristic
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—181no—
863C4—181no—
864C4—181no—
865C4—181no—
866C3—31no—
867C3—31no—
868C3—61no—
869C3C3×#570411yescharacteristic
870C2—41no—
871C2—182no—
872C2—361no—
873C2—361no—
874C2—361no—
875C2#41×(C3⋊D3)⋊C311yescharacteristic
876C2#1172263811yescharacteristic
877C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#126C2
hypercenter#126(C3⋊D3)⋊C3
hypocenterC32C3×#538
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. #64105⋊C3C2semidirect
4. #64104⋊C3C2semidirect
5. #64104⋊C3C2semidirect
6. #64103⋊C3C2semidirect
7. #64102⋊C3C2semidirect
8. #64094⋊C3C2semidirect
9. #64093⋊C3C2semidirect
10. #64092⋊C3C2semidirect
11. #64091⋊C3C2semidirect
12. #64091⋊C3C2semidirect
13. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
14. #64084⋊C3C2semidirect
15. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
16. #10596175C3semidirect
25. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×#634⋊C3C22semidirect
31. C4⋊C4×H(3,𝔽3)C22semidirect
32. C4⋊C4×H(3,𝔽3)C22semidirect
33. C4⋊C4×H(3,𝔽3)C22semidirect
37. C42×H(3,𝔽3)C22semidirect
45. #3752⋊C3C22semidirect
46. #3752⋊C3C22semidirect
47. #3752⋊C3C22semidirect
48. #3752⋊C3C22semidirect
49. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
50. #3750⋊C3C22semidirect
51. #3750⋊C3C22semidirect
52. C4×(C3⋊Dic3)⋊C3C22semidirect
54. C32×#126D3semidirect
55. C32×#126C2×C3semidirect
56. #64107C2×C3semidirect
57. #64105C2×C3semidirect
58. #64104C2×C3semidirect
59. #64104C2×C3semidirect
60. #64103C2×C3semidirect
61. #64102C2×C3semidirect
62. #64094C2×C3semidirect
63. #64093C2×C3semidirect
64. #64092C2×C3semidirect
65. #64091C2×C3semidirect
66. #64091C2×C3semidirect
67. C22⋊C4×C3⋊D3C2×C3semidirect
68. #64084C2×C3semidirect
69. C4×C4⋊(C3⋊D3)C2×C3semidirect
125. C2×C4⋊(C3⋊D3)C22×C3semidirect
128. C2×C4×C3⋊D3C22×C3semidirect
129. C2×C4×C3⋊D3C22×C3semidirect
130. C2×#634C22×C3semidirect
146. C32×C4⋊C4C2×D3semidirect
147. C32×C4⋊C4C2×D3semidirect
148. C32×C4⋊C4C2×D3semidirect
149. C32×C4⋊C4C22×C3semidirect
150. C32×C4⋊C4C22×C3semidirect
151. C32×C4⋊C4C22×C3semidirect
162. C32×C42C2×D3semidirect
163. C32×C42C22×C3semidirect
171. #3752C22×C3semidirect
172. #3752C22×C3semidirect
173. #3752C22×C3semidirect
174. #3752C22×C3semidirect
175. C4⋊(C3⋊Dic3)C22×C3semidirect
176. #3750C22×C3semidirect
177. #3750C22×C3semidirect
178. C4×C3⋊Dic3C22×C3semidirect
520. #126(C3⋊D3)⋊C3semidirect
534. H(3,𝔽3)#538semidirect
668. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
669. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
670. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
686. C42C2×(C3⋊D3)⋊C3semidirect
779. C32#5704semidirect
780. C32C3×#538semidirect

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
#64104⋊C32
#64103⋊C32
#64102⋊C32
#64094⋊C32
#64093⋊C32
#64092⋊C32
#64091⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64084⋊C32
C4×C4⋊((C3⋊D3)⋊C3)2
#105961753
C3×#57043