Finite Group Databasebeta

← #10596125⋊C3 #13153045

Subgroups — #10596125⋊C3 #13153045

Order 1728.

1247 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
4#64148⋊C3C211yesmaximal, characteristic, complemented
5C2×#3752⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C211yesmaximal, characteristic, complemented
7#64104⋊C3C211yesmaximal, characteristic, complemented
8#64103⋊C3C211yesmaximal, characteristic, complemented
9#64102⋊C3C211yesmaximal, characteristic, complemented
10#64094⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic, complemented
12#64091⋊C3C211yesmaximal, characteristic, complemented
13#64091⋊C3C211yesmaximal, characteristic, complemented
14#64090⋊C3C211yesmaximal, characteristic, complemented
15C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
16#10596125C311yesmaximal, characteristic, complemented
17C3×#5654—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C23×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×D4×H(3,𝔽3)C2211yescharacteristic
21C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic, complemented
25C2×#638⋊C3C2211yescharacteristic, complemented
26C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
27D4×(C3⋊D3)⋊C3—24no—
28#3828⋊C3—24no—
29C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
30C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
31C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
32C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
33C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
34C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
35C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
36C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
37C2×#634⋊C3C2211yescharacteristic, complemented
38C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
39C4⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
40C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
41C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
42C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
43#3757⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic
45#3752⋊C3C2211yescharacteristic
46#3752⋊C3C2211yescharacteristic
47#3752⋊C3C2211yescharacteristic, complemented
48#3752⋊C3C2211yescharacteristic, complemented
49#3752⋊C3C2211yescharacteristic, complemented
50#3752⋊C3C2211yescharacteristic, complemented
51#3752⋊C3C2211yescharacteristic, complemented
52#3750⋊C3C2211yescharacteristic, complemented
53#3750⋊C3C2211yescharacteristic, complemented
54C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
56C2×#3828C2×C311yescharacteristic, complemented
57C2×C3×D3×D4—31no—
58C2×C3×#235—31no—
59C32×#123—21no—
60C32×#123D311yescharacteristic, complemented
61C32×#123C2×C311yescharacteristic, complemented
62#64148C2×C311yescharacteristic, complemented
63C2×#3752C2×C311yescharacteristic, complemented
64#64105C2×C311yescharacteristic, complemented
65#64104C2×C311yescharacteristic, complemented
66#64103C2×C311yescharacteristic, complemented
67#64102C2×C311yescharacteristic, complemented
68#64094C2×C311yescharacteristic, complemented
69#64093C2×C311yescharacteristic, complemented
70#64091C2×C311yescharacteristic, complemented
71#64091C2×C311yescharacteristic, complemented
72#64090C2×C311yescharacteristic, complemented
73C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
74C3×#939—31no—
75C2×C3×(C2×D3)⋊C4—31no—
76C3×#896—31no—
77C3×#895—31no—
78C3×#894—31no—
79C3×#893—31no—
80C3×#885—31no—
81C3×#884—31no—
82C3×#882—31no—
83C3×#882—31no—
84C3×#67⋊C4—31no—
85C3×D3×C22⋊C4—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C23×H(3,𝔽3)C2311yescharacteristic
88C22×(C3⋊D3)⋊C3—22no—
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3—22no—
92C22×(C3⋊D3)⋊C3—41no—
93C22×(C3⋊D3)⋊C3—41no—
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C22×(C3⋊D3)⋊C3C2311yescharacteristic
96C22×(C3⋊D3)⋊C3C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98D4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)—22no—
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101C2×C4×H(3,𝔽3)C2311yescharacteristic
102C2×C4×H(3,𝔽3)C2311yescharacteristic
103C2×C4×H(3,𝔽3)C2311yescharacteristic
104C2×C4×H(3,𝔽3)C2311yescharacteristic
105#638⋊C3—22no—
106#638⋊C3—22no—
107#638⋊C3—41no—
108#638⋊C3D414yescomplemented
109C2×(C3⋊Dic3)⋊C3—41no—
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C4⋊((C3⋊D3)⋊C3)—22no—
115C4⋊((C3⋊D3)⋊C3)—22no—
116C4⋊((C3⋊D3)⋊C3)—22no—
117C4⋊((C3⋊D3)⋊C3)—41no—
118C4×(C3⋊D3)⋊C3—22no—
119C4×(C3⋊D3)⋊C3—22no—
120C4×(C3⋊D3)⋊C3—22no—
121C4×(C3⋊D3)⋊C3—41no—
122#634⋊C3—22no—
123C3×#546—91no—
124#5654—31no—
125#5654—91no—
126C23×C3⋊D3C22×C311yescharacteristic
127C23×C3⋊D3C22×C311yescharacteristic
128C23×C3×D3—31no—
129C23×C3×D3—31no—
130C2×C32×D4—21no—
131C2×C32×D4C2×D311yescharacteristic
132C2×C32×D4C22×C311yescharacteristic
133C22×C32×C4—21no—
134C22×C32×C4C2×D311yescharacteristic, complemented
135C22×C32×C4C22×C311yescharacteristic, complemented
136C2×#638C22×C311yescharacteristic
137C2×#638C22×C311yescharacteristic
138C2×#638C22×C311yescharacteristic, complemented
139C2×#638C22×C311yescharacteristic, complemented
140C22×C3⋊Dic3C22×C311yescharacteristic, complemented
141D4×C3⋊D3—24no—
142#3828—24no—
143C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
144C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
145C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
146C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
147C2×C4×C3⋊D3C22×C311yescharacteristic
148C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
149C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
150C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
151C2×#634C22×C311yescharacteristic, complemented
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C3×D3×D4—64no—
158C3×#235—64no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×Dic6—31no—
168C32×C4⋊C4—21no—
169C32×C4⋊C4—21no—
170C32×C4⋊C4C2×D311yescharacteristic, complemented
171C32×C4⋊C4C2×D311yescharacteristic, complemented
172C32×C4⋊C4C22×C311yescharacteristic, complemented
173C32×C4⋊C4C22×C311yescharacteristic, complemented
174C32×C22⋊C4—21no—
175C32×C22⋊C4—21no—
176C32×C22⋊C4—21no—
177C32×C22⋊C4C2×D311yescharacteristic, complemented
178C32×C22⋊C4C2×D311yescharacteristic, complemented
179C32×C22⋊C4C2×D311yescharacteristic, complemented
180C32×C22⋊C4C22×C311yescharacteristic, complemented
181C32×C22⋊C4C22×C311yescharacteristic, complemented
182C32×C22⋊C4C22×C311yescharacteristic, complemented
183#3757C22×C311yescharacteristic, complemented
184#3752C22×C311yescharacteristic
185#3752C22×C311yescharacteristic
186#3752C22×C311yescharacteristic
187#3752C22×C311yescharacteristic, complemented
188#3752C22×C311yescharacteristic, complemented
189#3752C22×C311yescharacteristic, complemented
190#3752C22×C311yescharacteristic, complemented
191#3752C22×C311yescharacteristic, complemented
192#3750C22×C311yescharacteristic, complemented
193#3750C22×C311yescharacteristic, complemented
194C4×C3⋊Dic3C22×C311yescharacteristic, complemented
195C3×#217—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×C4×Dic3—31no—
207C22×H(3,𝔽3)—21no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)—21no—
210C22×H(3,𝔽3)—21no—
211C22×H(3,𝔽3)—21no—
212C22×H(3,𝔽3)C2×D412yes—
213C22×H(3,𝔽3)C2411yescharacteristic
214C2×(C3⋊D3)⋊C3—21no—
215C2×(C3⋊D3)⋊C3—21no—
216C2×(C3⋊D3)⋊C3—21no—
217C2×(C3⋊D3)⋊C3—21no—
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—21no—
223C2×(C3⋊D3)⋊C3—21no—
224C2×(C3⋊D3)⋊C3—44no—
225C2×(C3⋊D3)⋊C3—44no—
226C2×(C3⋊D3)⋊C3C2×D412yes—
227C2×(C3⋊D3)⋊C3#4112yescomplemented
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230C4×H(3,𝔽3)—21no—
231C4×H(3,𝔽3)—21no—
232C4×H(3,𝔽3)—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3C2×D412yes—
237C2×C3×#41—91no—
238C22×C3×D4—91no—
239C2×D3×D4—31no—
240C2×D3×D4—91no—
241C2×#235—31no—
242C2×#235—91no—
243C3×#124—91no—
244C3×#123—31no—
245C3×#123—31no—
246C3×#123—61no—
247C3×#123—91no—
248C3×#123C3×D311yescharacteristic
249C3×C22⋊Q8—91no—
250C3×#121—91no—
251C3×#121—91no—
252C3×#121—91no—
253C3×#120—91no—
254C3×#120—91no—
255C3×C4×D4—91no—
256C3×C4×D4—91no—
257C2×C3×C22⋊C4—91no—
258C2×C3×C22⋊C4—91no—
259#939—31no—
260#939—91no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—91no—
263#896—31no—
264#896—91no—
265#895—31no—
266#895—91no—
267#894—31no—
268#894—91no—
269#893—31no—
270#893—91no—
271#885—31no—
272#885—91no—
273#884—31no—
274#884—91no—
275#882—31no—
276#882—31no—
277#882—91no—
278#882—91no—
279#67⋊C4—31no—
280#67⋊C4—91no—
281D3×C22⋊C4—31no—
282D3×C22⋊C4—91no—
283C23×C32—21no—
284C23×C32—21no—
285C23×C32C22×D311yescharacteristic
286C23×C32C22×D311yescharacteristic
287C23×C32C23×C311yescharacteristic
288C23×C32C23×C311yescharacteristic
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—41no—
294C22×C3⋊D3—41no—
295C22×C3⋊D3C23×C311yescharacteristic
296C22×C3⋊D3C23×C311yescharacteristic
297C22×C3⋊D3C23×C311yescharacteristic
298C22×C3⋊D3C23×C311yescharacteristic
299C22×C3×D3—31no—
300C22×C3×D3—31no—
301C22×C3×D3—31no—
302C22×C3×D3—31no—
303C22×C3×D3—62no—
304C22×C3×D3—62no—
305C22×C3×D3—62no—
306C22×C3×D3—62no—
307C22×C3×D3—121no—
308C22×C3×D3—121no—
309C32×D4—22no—
310C32×D4—22no—
311C32×D4—42no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319C2×C32×C4—42no—
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C22×D311yescharacteristic
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C22×D311yescharacteristic
325C2×C32×C4C23×C311yescharacteristic
326C2×C32×C4C23×C311yescharacteristic
327C2×C32×C4C23×C311yescharacteristic
328C2×C32×C4C23×C311yescharacteristic
329C2×C32×C4C23×C311yescharacteristic
330#638—22no—
331#638—22no—
332#638—41no—
333#638C3×D414yescomplemented
334C2×C3⋊Dic3—41no—
335C2×C3⋊Dic3C23×C311yescharacteristic
336C2×C3⋊Dic3C23×C311yescharacteristic
337C2×C3⋊Dic3C23×C311yescharacteristic
338C2×C3⋊Dic3C23×C311yescharacteristic
339C4⋊(C3⋊D3)—22no—
340C4⋊(C3⋊D3)—22no—
341C4⋊(C3⋊D3)—22no—
342C4⋊(C3⋊D3)—41no—
343C4×C3⋊D3—22no—
344C4×C3⋊D3—22no—
345C4×C3⋊D3—22no—
346C4×C3⋊D3—41no—
347#634—22no—
348C3×#67—34no—
349C3×#67—62no—
350C3×#67—62no—
351C3×#67—121no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—31no—
356C2×C3×Dic3—121no—
357C3×D12—62no—
358C3×D12—62no—
359C3×D12—62no—
360C3×D12—121no—
361C3×C4×D3—62no—
362C3×C4×D3—62no—
363C3×C4×D3—62no—
364C3×C4×D3—121no—
365C3×Dic6—62no—
366#546—91noSylow
367C2×H(3,𝔽3)—22no—
368C2×H(3,𝔽3)—41no—
369C2×H(3,𝔽3)C22×D411yescharacteristic
370C2×H(3,𝔽3)C2×#4111yescharacteristic
371C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
372(C3⋊D3)⋊C3—22no—
373(C3⋊D3)⋊C3—22no—
374(C3⋊D3)⋊C3—41no—
375(C3⋊D3)⋊C3—41no—
376C24×C3—91no—
377C24×C3—91no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—91no—
381C23×D3—91no—
382C3×#41—184no—
383C2×C3×Q8—91no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—61no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C2×C3×D4—91no—
391C2×C3×D4—91no—
392C2×C3×D4—91no—
393C2×C3×D4—91no—
394C2×C3×D4—91no—
395C2×C3×D4—184no—
396C2×C3×D4C2×C3×D311yescharacteristic
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—61no—
400C22×C3×C4—91no—
401C22×C3×C4—91no—
402C22×C3×C4—91no—
403C22×C3×C4—91no—
404C22×C3×C4—91no—
405C22×C3×C4C2×C3×D311yescharacteristic
406C2×#67—31no—
407C2×#67—31no—
408C2×#67—31no—
409C2×#67—31no—
410C2×#67—91no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C22×Dic3—31no—
415C22×Dic3—91no—
416D3×D4—64no—
417D3×D4—184no—
418#235—64no—
419#235—184no—
420C2×D12—31no—
421C2×D12—31no—
422C2×D12—31no—
423C2×D12—31no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—91no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×Dic6—31no—
437C2×Dic6—91no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—61no—
443C3×C4⋊C4—61no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4C2×C3×D311yescharacteristic
447C3×C4⋊C4C2×C3×D311yescharacteristic
448C3×C22⋊C4—31no—
449C3×C22⋊C4—31no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—61no—
455C3×C22⋊C4—61no—
456C3×C22⋊C4—61no—
457C3×C22⋊C4—91no—
458C3×C22⋊C4—91no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C22⋊C4—91no—
463C3×C22⋊C4—91no—
464C3×C22⋊C4—91no—
465C3×C22⋊C4—91no—
466C3×C22⋊C4C2×C3×D311yescharacteristic
467C3×C22⋊C4C2×C3×D311yescharacteristic
468C3×C22⋊C4C2×C3×D311yescharacteristic
469C3×C42—91no—
470#217—31no—
471#217—91no—
472(C2×D3)⋊C4—31no—
473(C2×D3)⋊C4—31no—
474(C2×D3)⋊C4—31no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487(C2×D3)⋊C4—91no—
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492C4×Dic3—31no—
493C4×Dic3—91no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—22no—
506C22×C32—41no—
507C22×C32—41no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32D3×D412yes—
512C22×C32C2×C3×D412yes—
513C22×C32C23×D311yescharacteristic
514C22×C32C24×C311yescharacteristic
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3—21no—
518C2×C3⋊D3—21no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—44no—
526C2×C3⋊D3—44no—
527C2×C3⋊D3C2×C3×D412yes—
528C2×C3⋊D3C3×#4112yescomplemented
529C2×C3×D3—32no—
530C2×C3×D3—32no—
531C2×C3×D3—61no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—124no—
542C2×C3×D3—124no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—21no—
548C32×C4—21no—
549C32×C4—21no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—41no—
554C32×C4—41no—
555C32×C4—41no—
556C32×C4—41no—
557C32×C4—41no—
558C3⋊Dic3—21no—
559C3⋊Dic3—21no—
560C3⋊Dic3—21no—
561C3⋊Dic3C2×C3×D412yes—
562C3×Dic3—32no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C2×#41—91no—
567C22×D4—91no—
568#124—91no—
569#123—91no—
570#123(C3⋊D3)⋊C311yescharacteristic, complemented
571C22⋊Q8—91no—
572#121—91no—
573#121—91no—
574#121—91no—
575#120—91no—
576#120—91no—
577C4×D4—91no—
578C4×D4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—31no—
585C23×C3—31no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—91no—
589C23×C3—91no—
590C23×C3—91no—
591C23×C3—91no—
592C23×C3—182no—
593C23×C3—182no—
594C23×C3—182no—
595C23×C3—182no—
596C23×C3—361no—
597C23×C3—361no—
598C23×C3C22×C3×D311yescharacteristic
599C23×C3C22×C3×D311yescharacteristic
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—91no—
609C22×D3—91no—
610C22×D3—91no—
611C22×D3—91no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—361no—
619C22×D3—361no—
620C3×Q8—182no—
621C3×D4—22no—
622C3×D4—62no—
623C3×D4—62no—
624C3×D4—94no—
625C3×D4—122no—
626C3×D4—182no—
627C3×D4—182no—
628C3×D4—182no—
629C3×D4—182no—
630C3×D4—182no—
631C3×D4—361no—
632C3×D4—361no—
633C2×C3×C4—22no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—91no—
652C2×C3×C4—91no—
653C2×C3×C4—91no—
654C2×C3×C4—91no—
655C2×C3×C4—122no—
656C2×C3×C4—182no—
657C2×C3×C4—182no—
658C2×C3×C4—182no—
659C2×C3×C4—361no—
660C2×C3×C4—361no—
661C2×C3×C4C22×C3×D311yescharacteristic
662C2×C3×C4C22×C3×D311yescharacteristic
663C2×C3×C4C22×C3×D311yescharacteristic
664C2×C3×C4C22×C3×D311yescharacteristic
665C2×C3×C4C22×C3×D311yescharacteristic
666#67—34no—
667#67—62no—
668#67—62no—
669#67—94no—
670#67—121no—
671#67—182no—
672#67—182no—
673#67—361no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—91no—
679C2×Dic3—91no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—121no—
683C2×Dic3—361no—
684D12—62no—
685D12—62no—
686D12—62no—
687D12—121no—
688D12—182no—
689D12—182no—
690D12—182no—
691D12—361no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—62no—
695C4×D3—121no—
696C4×D3—182no—
697C4×D3—182no—
698C4×D3—182no—
699C4×D3—361no—
700Dic6—62no—
701Dic6—182no—
702C2×C32—22no—
703C2×C32—22no—
704C2×C32—21no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—42no—
708C2×C32—41no—
709C2×C32—41no—
710C2×C32—81no—
711C2×C32C2×D3×D411yescharacteristic
712C2×C32D3×#4111yescharacteristic
713C2×C32#100911yescharacteristic
714C2×C32C22×C3×D411yescharacteristic
715C2×C32C2×C3×#4111yescharacteristic
716C2×C32C3×H(5,𝔽2)11yescharacteristic
717C3⋊D3—22no—
718C3⋊D3—22no—
719C3⋊D3—41no—
720C3⋊D3—41no—
721C3×D3—62no—
722C3×D3—62no—
723C3×D3—121no—
724C3×D3—121no—
725C24—91no—
726C24—91no—
727#41—184no—
728C2×Q8—91no—
729C2×D4—91no—
730C2×D4—91no—
731C2×D4—91no—
732C2×D4—91no—
733C2×D4—91no—
734C2×D4—91no—
735C2×D4—91no—
736C2×D4—91no—
737C2×D4—184no—
738C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
748C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
749C22⋊C4—91no—
750C22⋊C4—91no—
751C22⋊C4—91no—
752C22⋊C4—91no—
753C22⋊C4—91no—
754C22⋊C4—91no—
755C22⋊C4—91no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
759C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
760C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
761C42—91no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—31no—
768C22×C3—31no—
769C22×C3—32no—
770C22×C3—32no—
771C22×C3—61no—
772C22×C3—61no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—62no—
783C22×C3—92no—
784C22×C3—92no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—181no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—181no—
800C22×C3—364no—
801C22×C3—364no—
802C22×C3C3×D3×D412yes—
803C22×C3C23×C3×D311yescharacteristic
804C2×D3—32no—
805C2×D3—32no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—92no—
817C2×D3—92no—
818C2×D3—124no—
819C2×D3—124no—
820C2×D3—181no—
821C2×D3—181no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—181no—
827C2×D3—181no—
828C2×D3—181no—
829C2×D3—181no—
830C2×D3—364no—
831C2×D3—364no—
832C3×C4—21no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—61no—
838C3×C4—61no—
839C3×C4—61no—
840C3×C4—61no—
841C3×C4—61no—
842C3×C4—61no—
843C3×C4—61no—
844C3×C4—61no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—92no—
848C3×C4—121no—
849C3×C4—121no—
850C3×C4—121no—
851C3×C4—121no—
852C3×C4—121no—
853C3×C4—181no—
854C3×C4—181no—
855C3×C4—181no—
856Dic3—32no—
857Dic3—61no—
858Dic3—61no—
859Dic3—61no—
860Dic3—92no—
861Dic3—181no—
862Dic3—181no—
863Dic3—181no—
864C32—21no—
865C32#565411yescharacteristic, complemented
866C32C3×#54611yescharacteristic, complemented
867C23—91no—
868C23—91no—
869C23—91no—
870C23—91no—
871C23—182no—
872C23—182no—
873C23—182no—
874C23—182no—
875C23—361no—
876C23—361no—
877C23C22×(C3⋊D3)⋊C311yescharacteristic
878C23C22×(C3⋊D3)⋊C311yescharacteristic
879Q8—182no—
880D4—22no—
881D4—94no—
882D4—182no—
883D4—182no—
884D4—182no—
885D4—182no—
886D4—182no—
887D4—361no—
888D4—361no—
889C2×C4—22no—
890C2×C4—91no—
891C2×C4—91no—
892C2×C4—91no—
893C2×C4—91no—
894C2×C4—182no—
895C2×C4—182no—
896C2×C4—182no—
897C2×C4—361no—
898C2×C4—361no—
899C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
900C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
901C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
902C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
903C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
904C2×C3—22no—
905C2×C3—31no—
906C2×C3—31no—
907C2×C3—31no—
908C2×C3—31no—
909C2×C3—31no—
910C2×C3—31no—
911C2×C3—41no—
912C2×C3—62no—
913C2×C3—62no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—61no—
917C2×C3—122no—
918C2×C3—121no—
919C2×C3—121no—
920C2×C3—182no—
921C2×C3—182no—
922C2×C3—241no—
923C2×C3—361no—
924C2×C3—361no—
925C2×C3C2×C3×D3×D411yescharacteristic
926C2×C3C3×D3×#4111yescharacteristic
927C2×C3C3×#100911yescharacteristic
928D3—62no—
929D3—62no—
930D3—121no—
931D3—121no—
932D3—182no—
933D3—182no—
934D3—361no—
935D3—361no—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—92no—
942C22—92no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—364no—
954C22—364no—
955C22D4×(C3⋊D3)⋊C312yes—
956C22C23×(C3⋊D3)⋊C311yescharacteristic
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—92no—
963C4—181no—
964C4—181no—
965C4—181no—
966C3—31no—
967C3—31no—
968C3—61no—
969C3C3×#565411yescharacteristic
970C2—22no—
971C2—41no—
972C2—182no—
973C2—182no—
974C2—361no—
975C2—361no—
976C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
977C2#41×(C3⋊D3)⋊C311yescharacteristic
978C2#1172263811yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×D4×(C3⋊D3)⋊C3C2semidirect
2. C2×#3828⋊C3C2semidirect
3. H(3,𝔽3)×#123C2semidirect
4. #64148⋊C3C2semidirect
5. C2×#3752⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64104⋊C3C2semidirect
8. #64103⋊C3C2semidirect
9. #64102⋊C3C2semidirect
10. #64094⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #64091⋊C3C2semidirect
13. #64091⋊C3C2semidirect
14. #64090⋊C3C2semidirect
15. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
16. #10596125C3semidirect
21. C22×C4×H(3,𝔽3)C22semidirect
24. C2×#638⋊C3C22semidirect
25. C2×#638⋊C3C22semidirect
26. C22×(C3⋊Dic3)⋊C3C22semidirect
31. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
32. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
34. C2×C4×(C3⋊D3)⋊C3C22semidirect
35. C2×C4×(C3⋊D3)⋊C3C22semidirect
36. C2×C4×(C3⋊D3)⋊C3C22semidirect
37. C2×#634⋊C3C22semidirect
38. C4⋊C4×H(3,𝔽3)C22semidirect
39. C4⋊C4×H(3,𝔽3)C22semidirect
40. C22⋊C4×H(3,𝔽3)C22semidirect
41. C22⋊C4×H(3,𝔽3)C22semidirect
42. C22⋊C4×H(3,𝔽3)C22semidirect
43. #3757⋊C3C22semidirect
47. #3752⋊C3C22semidirect
48. #3752⋊C3C22semidirect
49. #3752⋊C3C22semidirect
50. #3752⋊C3C22semidirect
51. #3752⋊C3C22semidirect
52. #3750⋊C3C22semidirect
53. #3750⋊C3C22semidirect
54. C4×(C3⋊Dic3)⋊C3C22semidirect
55. C2×D4×C3⋊D3C2×C3semidirect
56. C2×#3828C2×C3semidirect
60. C32×#123D3semidirect
61. C32×#123C2×C3semidirect
62. #64148C2×C3semidirect
63. C2×#3752C2×C3semidirect
64. #64105C2×C3semidirect
65. #64104C2×C3semidirect
66. #64103C2×C3semidirect
67. #64102C2×C3semidirect
68. #64094C2×C3semidirect
69. #64093C2×C3semidirect
70. #64091C2×C3semidirect
71. #64091C2×C3semidirect
72. #64090C2×C3semidirect
73. C22⋊C4×C3⋊D3C2×C3semidirect
108. #638⋊C3D4semidirect
134. C22×C32×C4C2×D3semidirect
135. C22×C32×C4C22×C3semidirect
138. C2×#638C22×C3semidirect
139. C2×#638C22×C3semidirect
140. C22×C3⋊Dic3C22×C3semidirect
145. C2×C4⋊(C3⋊D3)C22×C3semidirect
146. C2×C4⋊(C3⋊D3)C22×C3semidirect
148. C2×C4×C3⋊D3C22×C3semidirect
149. C2×C4×C3⋊D3C22×C3semidirect
150. C2×C4×C3⋊D3C22×C3semidirect
151. C2×#634C22×C3semidirect
170. C32×C4⋊C4C2×D3semidirect
171. C32×C4⋊C4C2×D3semidirect
172. C32×C4⋊C4C22×C3semidirect
173. C32×C4⋊C4C22×C3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C2×D3semidirect
179. C32×C22⋊C4C2×D3semidirect
180. C32×C22⋊C4C22×C3semidirect
181. C32×C22⋊C4C22×C3semidirect
182. C32×C22⋊C4C22×C3semidirect
183. #3757C22×C3semidirect
187. #3752C22×C3semidirect
188. #3752C22×C3semidirect
189. #3752C22×C3semidirect
190. #3752C22×C3semidirect
191. #3752C22×C3semidirect
192. #3750C22×C3semidirect
193. #3750C22×C3semidirect
194. C4×C3⋊Dic3C22×C3semidirect
227. C2×(C3⋊D3)⋊C3#41semidirect
333. #638C3×D4semidirect
528. C2×C3⋊D3C3×#41semidirect
570. #123(C3⋊D3)⋊C3semidirect
581. H(3,𝔽3)#546semidirect
744. C22×C4C2×(C3⋊D3)⋊C3semidirect
747. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
748. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
758. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
759. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
760. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
865. C32#5654semidirect
866. C32C3×#546semidirect

Maximal subgroups

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

subgroupindex
C2×D4×(C3⋊D3)⋊C32
C2×#3828⋊C32
H(3,𝔽3)×#1232
#64148⋊C32
C2×#3752⋊C32
#64105⋊C32
#64104⋊C32
#64103⋊C32
#64102⋊C32
#64094⋊C32
#64093⋊C32
#64091⋊C32
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#105961253
C3×#56543