Finite Group Databasebeta

← #10595961⋊C3 #13152366

Subgroups — #10595961⋊C3 #13152366

Order 1728.

1301 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#638⋊C3C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
4#11721702C211yesmaximal, characteristic, complemented
5#64139⋊C3C211yesmaximal, characteristic, complemented
6#64138⋊C3C211yesmaximal, characteristic, complemented
7C4×#638⋊C3C211yesmaximal, characteristic, complemented
8#64094⋊C3C211yesmaximal, characteristic, complemented
9#64093⋊C3C211yesmaximal, characteristic, complemented
10#64093⋊C3C211yesmaximal, characteristic, complemented
11#64092⋊C3C211yesmaximal, characteristic, complemented
12#64091⋊C3C211yesmaximal, characteristic, complemented
13#64090⋊C3C211yesmaximal, characteristic, complemented
14C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
15#64087⋊C3C211yesmaximal, characteristic, complemented
16#10595961C311yesmaximal, characteristic, complemented
17C3×#5490—31nomaximal
18C24×H(3,𝔽3)C2211yescharacteristic
19C23×(C3⋊D3)⋊C3C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
22C2×#638⋊C3—24no—
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C2×#638⋊C3C2211yescharacteristic
26C2×#638⋊C3C2211yescharacteristic
27C2×#638⋊C3C2211yescharacteristic
28C2×#638⋊C3C2211yescharacteristic, complemented
29C2×#638⋊C3C2211yescharacteristic, complemented
30C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
31#3828⋊C3—24no—
32C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
33C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
34C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
35C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
36C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
37C2×#634⋊C3C2211yescharacteristic, complemented
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic
39C22⋊C4×H(3,𝔽3)C2211yescharacteristic
40C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
41C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic
43#3757⋊C3C2211yescharacteristic, complemented
44#3757⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46#3752⋊C3C2211yescharacteristic, complemented
47#3752⋊C3C2211yescharacteristic, complemented
48#3752⋊C3C2211yescharacteristic, complemented
49#3752⋊C3C2211yescharacteristic, complemented
50C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
51#3750⋊C3C2211yescharacteristic, complemented
52#3750⋊C3C2211yescharacteristic, complemented
53#3750⋊C3C2211yescharacteristic, complemented
54C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
55C22×#638C2×C311yescharacteristic, complemented
56C2×#3828C2×C311yescharacteristic, complemented
57C22×C3×#67—31no—
58C2×C3×#235—31no—
59C2×C32×C22⋊C4—21no—
60C2×C32×C22⋊C4D311yescharacteristic, complemented
61C2×C32×C22⋊C4C2×C311yescharacteristic, complemented
62#64162C2×C311yescharacteristic, complemented
63#64139C2×C311yescharacteristic, complemented
64#64138C2×C311yescharacteristic, complemented
65C4×#638C2×C311yescharacteristic, complemented
66#64094C2×C311yescharacteristic, complemented
67#64093C2×C311yescharacteristic, complemented
68#64093C2×C311yescharacteristic, complemented
69#64092C2×C311yescharacteristic, complemented
70#64091C2×C311yescharacteristic, complemented
71#64090C2×C311yescharacteristic, complemented
72C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
73#64087C2×C311yescharacteristic, complemented
74C3×#953—31no—
75C3×#930—31no—
76C3×#929—31no—
77C3×C4×#67—31no—
78C3×#885—31no—
79C3×#884—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#882—31no—
83C3×#67⋊C4—31no—
84C3×D3×C22⋊C4—31no—
85C3×#878—31no—
86C23×H(3,𝔽3)—22no—
87C23×H(3,𝔽3)—22no—
88C23×H(3,𝔽3)—41no—
89C23×H(3,𝔽3)C2311yescharacteristic
90C23×H(3,𝔽3)C2311yescharacteristic
91C23×H(3,𝔽3)C2311yescharacteristic
92C22×(C3⋊D3)⋊C3—22no—
93C22×(C3⋊D3)⋊C3—22no—
94C22×(C3⋊D3)⋊C3—41no—
95C22×(C3⋊D3)⋊C3C2311yescharacteristic
96C22×(C3⋊D3)⋊C3C2311yescharacteristic
97C22×(C3⋊D3)⋊C3C2311yescharacteristic
98C2×C4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)—41no—
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101C2×C4×H(3,𝔽3)C2311yescharacteristic
102C2×C4×H(3,𝔽3)C2311yescharacteristic
103C2×C4×H(3,𝔽3)C2311yescharacteristic
104#638⋊C3—22no—
105#638⋊C3—22no—
106#638⋊C3—22no—
107#638⋊C3—22no—
108#638⋊C3—22no—
109#638⋊C3—41no—
110#638⋊C3D414yescomplemented
111C2×(C3⋊Dic3)⋊C3—22no—
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
115C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
116C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
117C4⋊((C3⋊D3)⋊C3)—22no—
118C4⋊((C3⋊D3)⋊C3)—41no—
119C4×(C3⋊D3)⋊C3—22no—
120C4×(C3⋊D3)⋊C3—22no—
121C4×(C3⋊D3)⋊C3—41no—
122#634⋊C3—22no—
123C3×#546—91no—
124#5490—31no—
125#5490—91no—
126C24×C32—21no—
127C24×C32C2×D311yescharacteristic
128C24×C32C22×C311yescharacteristic
129C23×C3⋊D3C22×C311yescharacteristic
130C23×C3×D3—31no—
131C22×C32×C4—21no—
132C22×C32×C4—21no—
133C22×C32×C4C2×D311yescharacteristic, complemented
134C22×C32×C4C2×D311yescharacteristic, complemented
135C22×C32×C4C22×C311yescharacteristic, complemented
136C22×C32×C4C22×C311yescharacteristic, complemented
137C2×#638—24no—
138C2×#638C22×C311yescharacteristic
139C2×#638C22×C311yescharacteristic
140C2×#638C22×C311yescharacteristic
141C2×#638C22×C311yescharacteristic
142C2×#638C22×C311yescharacteristic
143C2×#638C22×C311yescharacteristic, complemented
144C2×#638C22×C311yescharacteristic, complemented
145C22×C3⋊Dic3C22×C311yescharacteristic
146#3828—24no—
147C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
148C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
149C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
150C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
151C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
152C2×#634C22×C311yescharacteristic, complemented
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—64no—
161C22×C3×Dic3—31no—
162C3×#235—64no—
163C2×C3×D12—31no—
164C2×C3×D12—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×Dic6—31no—
169C32×C22⋊C4—21no—
170C32×C22⋊C4—21no—
171C32×C22⋊C4—21no—
172C32×C22⋊C4—21no—
173C32×C22⋊C4C2×D311yescharacteristic
174C32×C22⋊C4C2×D311yescharacteristic
175C32×C22⋊C4C2×D311yescharacteristic, complemented
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177C32×C22⋊C4C22×C311yescharacteristic
178C32×C22⋊C4C22×C311yescharacteristic
179C32×C22⋊C4C22×C311yescharacteristic, complemented
180C32×C22⋊C4C22×C311yescharacteristic, complemented
181#3757C22×C311yescharacteristic
182#3757C22×C311yescharacteristic, complemented
183#3757C22×C311yescharacteristic, complemented
184#3752C22×C311yescharacteristic, complemented
185#3752C22×C311yescharacteristic, complemented
186#3752C22×C311yescharacteristic, complemented
187#3752C22×C311yescharacteristic, complemented
188#3752C22×C311yescharacteristic, complemented
189C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
190#3750C22×C311yescharacteristic, complemented
191#3750C22×C311yescharacteristic, complemented
192#3750C22×C311yescharacteristic, complemented
193C4×C3⋊Dic3C22×C311yescharacteristic, complemented
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—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×C4⋊Dic3—31no—
203C3×Dic3⋊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)—21no—
213C22×H(3,𝔽3)—21no—
214C22×H(3,𝔽3)—44no—
215C22×H(3,𝔽3)C2×D412yes—
216C22×H(3,𝔽3)#4112yescomplemented
217C22×H(3,𝔽3)C2411yescharacteristic
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—21no—
225C2×(C3⋊D3)⋊C3—21no—
226C2×(C3⋊D3)⋊C3—44no—
227C2×(C3⋊D3)⋊C3C2×D412yes—
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230C4×H(3,𝔽3)—21no—
231C4×H(3,𝔽3)—21no—
232(C3⋊Dic3)⋊C3—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—
239C22×#67—31no—
240C22×#67—91no—
241C2×#235—31no—
242C2×#235—91no—
243C3×#124—91no—
244C3×#123—91no—
245C3×#123—91no—
246C3×C22⋊Q8—91no—
247C3×#121—91no—
248C3×#121—91no—
249C3×#121—91no—
250C3×#120—91no—
251C3×#120—91no—
252C3×C4×D4—91no—
253C3×C4×D4—91no—
254C2×C3×C22⋊C4—31no—
255C2×C3×C22⋊C4—31no—
256C2×C3×C22⋊C4—61no—
257C2×C3×C22⋊C4—91no—
258C2×C3×C22⋊C4C3×D311yescharacteristic
259#953—31no—
260#953—91no—
261#930—31no—
262#930—91no—
263#929—31no—
264#929—91no—
265C4×#67—31no—
266C4×#67—91no—
267#885—31no—
268#885—91no—
269#884—31no—
270#884—31no—
271#884—91no—
272#884—91no—
273#883—31no—
274#883—91no—
275#882—31no—
276#882—91no—
277#67⋊C4—31no—
278#67⋊C4—91no—
279D3×C22⋊C4—31no—
280D3×C22⋊C4—91no—
281#878—31no—
282#878—91no—
283C23×C32—24no—
284C23×C32—22no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32—21no—
289C23×C32—21no—
290C23×C32—21no—
291C23×C32—42no—
292C23×C32—41no—
293C23×C32—41no—
294C23×C32—42no—
295C23×C32C22×D311yescharacteristic
296C23×C32C22×D311yescharacteristic
297C23×C32C22×D311yescharacteristic
298C23×C32C23×C311yescharacteristic
299C23×C32C23×C311yescharacteristic
300C23×C32C23×C311yescharacteristic
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—41no—
304C22×C3⋊D3C23×C311yescharacteristic
305C22×C3⋊D3C23×C311yescharacteristic
306C22×C3⋊D3C23×C311yescharacteristic
307C22×C3×D3—31no—
308C22×C3×D3—31no—
309C22×C3×D3—31no—
310C22×C3×D3—62no—
311C22×C3×D3—62no—
312C22×C3×D3—121no—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—21no—
318C2×C32×C4—21no—
319C2×C32×C4—42no—
320C2×C32×C4—41no—
321C2×C32×C4—41no—
322C2×C32×C4—42no—
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C22×D311yescharacteristic
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327C2×C32×C4C23×C311yescharacteristic
328C2×C32×C4C23×C311yescharacteristic
329C2×C32×C4C23×C311yescharacteristic
330C2×C32×C4C23×C311yescharacteristic
331#638—22no—
332#638—22no—
333#638—22no—
334#638—22no—
335#638—22no—
336#638—41no—
337#638C3×D414yescomplemented
338C2×C3⋊Dic3—22no—
339C2×C3⋊Dic3C23×C311yescharacteristic
340C2×C3⋊Dic3C23×C311yescharacteristic
341C2×C3⋊Dic3C23×C311yescharacteristic
342C2×C3⋊Dic3C23×C311yescharacteristic
343C2×C3⋊Dic3C23×C311yescharacteristic
344C4⋊(C3⋊D3)—22no—
345C4⋊(C3⋊D3)—41no—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—22no—
348C4×C3⋊D3—41no—
349#634—22no—
350C3×#67—34no—
351C3×#67—62no—
352C3×#67—62no—
353C3×#67—62no—
354C3×#67—62no—
355C3×#67—62no—
356C3×#67—121no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—31no—
359C2×C3×Dic3—31no—
360C2×C3×Dic3—31no—
361C2×C3×Dic3—31no—
362C2×C3×Dic3—62no—
363C3×D12—62no—
364C3×D12—121no—
365C3×C4×D3—62no—
366C3×C4×D3—62no—
367C3×C4×D3—121no—
368C3×Dic6—62no—
369#546—91noSylow
370C2×H(3,𝔽3)—22no—
371C2×H(3,𝔽3)—22no—
372C2×H(3,𝔽3)—41no—
373C2×H(3,𝔽3)C22×D411yescharacteristic
374C2×H(3,𝔽3)C2×#4111yescharacteristic
375C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
376(C3⋊D3)⋊C3—22no—
377(C3⋊D3)⋊C3—41no—
378(C3⋊D3)⋊C3—41no—
379C24×C3—31no—
380C24×C3—31no—
381C24×C3—61no—
382C24×C3—91no—
383C24×C3C2×C3×D311yescharacteristic
384C23×D3—31no—
385C23×D3—91no—
386C3×#41—184no—
387C2×C3×Q8—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—91no—
396C2×C3×D4—91no—
397C2×C3×D4—184no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4—91no—
405C22×C3×C4—91no—
406C22×C3×C4—91no—
407C22×C3×C4—91no—
408C22×C3×C4C2×C3×D311yescharacteristic
409C22×C3×C4C2×C3×D311yescharacteristic
410C2×#67—31no—
411C2×#67—31no—
412C2×#67—31no—
413C2×#67—31no—
414C2×#67—31no—
415C2×#67—31no—
416C2×#67—31no—
417C2×#67—64no—
418C2×#67—91no—
419C2×#67—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—91no—
423C2×#67—91no—
424C2×#67—91no—
425C2×#67—184no—
426C22×Dic3—31no—
427C22×Dic3—91no—
428#235—64no—
429#235—184no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—91no—
433C2×D12—91no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×Dic6—31no—
441C2×Dic6—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C22⋊C4—31no—
447C3×C22⋊C4—31no—
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—61no—
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×C22⋊C4C2×C3×D311yescharacteristic
470C3×C42—91no—
471#217—31no—
472#217—31no—
473#217—31no—
474#217—91no—
475#217—91no—
476#217—91no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—31no—
480(C2×D3)⋊C4—31no—
481(C2×D3)⋊C4—31no—
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—
487C4⋊Dic3—31no—
488C4⋊Dic3—91no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495C4×Dic3—31no—
496C4×Dic3—91no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—21no—
506C22×C32—21no—
507C22×C32—22no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—21no—
515C22×C32—22no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32—44no—
522C22×C32—44no—
523C22×C32—48no—
524C22×C32#23512yescomplemented
525C22×C32D3×D412yes—
526C22×C32C2×C3×D412yes—
527C22×C32C3×#4112yescomplemented
528C22×C32C23×D311yescharacteristic
529C22×C32C24×C311yescharacteristic
530C2×C3⋊D3—21no—
531C2×C3⋊D3—21no—
532C2×C3⋊D3—21no—
533C2×C3⋊D3—21no—
534C2×C3⋊D3—21no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—44no—
539C2×C3⋊D3C2×C3×D412yes—
540C2×C3×D3—32no—
541C2×C3×D3—61no—
542C2×C3×D3—61no—
543C2×C3×D3—61no—
544C2×C3×D3—61no—
545C2×C3×D3—61no—
546C2×C3×D3—61no—
547C2×C3×D3—61no—
548C2×C3×D3—61no—
549C2×C3×D3—124no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—41no—
559C32×C4—41no—
560C32×C4—41no—
561C32×C4—41no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3—21no—
566C3⋊Dic3C2×C3×D412yes—
567C3×Dic3—32no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—61no—
571C3×Dic3—61no—
572C2×#41—91no—
573C22×D4—91no—
574#124—91no—
575#123—91no—
576#123—91no—
577C22⋊Q8—91no—
578#121—91no—
579#121—91no—
580#121—91no—
581#120—91no—
582#120—91no—
583C4×D4—91no—
584C4×D4—91no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4(C3⋊D3)⋊C311yescharacteristic, complemented
587H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—31no—
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—31no—
596C23×C3—41no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—64no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—91no—
606C23×C3—91no—
607C23×C3—91no—
608C23×C3—122no—
609C23×C3—121no—
610C23×C3—121no—
611C23×C3—122no—
612C23×C3—182no—
613C23×C3—182no—
614C23×C3—361no—
615C23×C3C22×C3×D311yescharacteristic
616C23×C3C22×C3×D311yescharacteristic
617C23×C3C22×C3×D311yescharacteristic
618C22×D3—31no—
619C22×D3—31no—
620C22×D3—31no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—91no—
624C22×D3—91no—
625C22×D3—91no—
626C22×D3—121no—
627C22×D3—182no—
628C22×D3—182no—
629C22×D3—361no—
630C3×Q8—182no—
631C3×D4—94no—
632C3×D4—182no—
633C3×D4—182no—
634C3×D4—182no—
635C3×D4—182no—
636C3×D4—182no—
637C3×D4—182no—
638C3×D4—361no—
639C3×D4—361no—
640C2×C3×C4—22no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—31no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—31no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—41no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—91no—
659C2×C3×C4—91no—
660C2×C3×C4—91no—
661C2×C3×C4—122no—
662C2×C3×C4—121no—
663C2×C3×C4—121no—
664C2×C3×C4—122no—
665C2×C3×C4—182no—
666C2×C3×C4—182no—
667C2×C3×C4—182no—
668C2×C3×C4—361no—
669C2×C3×C4C22×C3×D311yescharacteristic
670C2×C3×C4C22×C3×D311yescharacteristic
671C2×C3×C4C22×C3×D311yescharacteristic
672C2×C3×C4C22×C3×D311yescharacteristic
673#67—34no—
674#67—62no—
675#67—62no—
676#67—62no—
677#67—62no—
678#67—62no—
679#67—94no—
680#67—121no—
681#67—182no—
682#67—182no—
683#67—182no—
684#67—182no—
685#67—182no—
686#67—361no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—62no—
693C2×Dic3—91no—
694C2×Dic3—91no—
695C2×Dic3—91no—
696C2×Dic3—91no—
697C2×Dic3—91no—
698C2×Dic3—182no—
699D12—62no—
700D12—121no—
701D12—182no—
702D12—361no—
703C4×D3—62no—
704C4×D3—62no—
705C4×D3—121no—
706C4×D3—182no—
707C4×D3—182no—
708C4×D3—361no—
709Dic6—62no—
710Dic6—182no—
711C2×C32—24no—
712C2×C32—22no—
713C2×C32—22no—
714C2×C32—22no—
715C2×C32—22no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—42no—
720C2×C32—42no—
721C2×C32—41no—
722C2×C32—41no—
723C2×C32C2×#23511yescharacteristic
724C2×C32C2×D3×D411yescharacteristic
725C2×C32#100411yescharacteristic
726C2×C32C22×C3×D411yescharacteristic
727C2×C32C2×C3×#4111yescharacteristic
728C2×C32C3×H(5,𝔽2)11yescharacteristic
729C3⋊D3—22no—
730C3⋊D3—41no—
731C3⋊D3—41no—
732C3×D3—62no—
733C3×D3—121no—
734C3×D3—121no—
735C24—91no—
736C24C2×(C3⋊D3)⋊C311yescharacteristic
737#41—184no—
738C2×Q8—91no—
739C2×D4—91no—
740C2×D4—91no—
741C2×D4—91no—
742C2×D4—91no—
743C2×D4—91no—
744C2×D4—91no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—91no—
748C2×D4—184no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4—91no—
753C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
754C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
755C4⋊C4—91no—
756C4⋊C4—91no—
757C4⋊C4—91no—
758C4⋊C4—91no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C22⋊C4—91no—
763C22⋊C4—91no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
768C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
769C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
770C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
771C42—91no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—31no—
780C22×C3—31no—
781C22×C3—32no—
782C22×C3—32no—
783C22×C3—32no—
784C22×C3—32no—
785C22×C3—44no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—61no—
789C22×C3—61no—
790C22×C3—61no—
791C22×C3—61no—
792C22×C3—61no—
793C22×C3—61no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—61no—
797C22×C3—61no—
798C22×C3—61no—
799C22×C3—61no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—61no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—92no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—124no—
812C22×C3—124no—
813C22×C3—128no—
814C22×C3—181no—
815C22×C3—181no—
816C22×C3—181no—
817C22×C3—181no—
818C22×C3—181no—
819C22×C3—181no—
820C22×C3—181no—
821C22×C3—181no—
822C22×C3—364no—
823C22×C3C3×#23512yes—
824C22×C3C3×D3×D412yes—
825C22×C3C23×C3×D311yescharacteristic
826C2×D3—32no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—61no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—92no—
836C2×D3—124no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—181no—
844C2×D3—181no—
845C2×D3—364no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—21no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—92no—
859C3×C4—121no—
860C3×C4—121no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866C3×C4—181no—
867Dic3—32no—
868Dic3—61no—
869Dic3—61no—
870Dic3—61no—
871Dic3—61no—
872Dic3—92no—
873Dic3—181no—
874Dic3—181no—
875Dic3—181no—
876Dic3—181no—
877C32—21no—
878C32#549011yescharacteristic, complemented
879C32C3×#54611yescharacteristic, complemented
880C23—22no—
881C23—22no—
882C23—41no—
883C23—91no—
884C23—91no—
885C23—91no—
886C23—182no—
887C23—182no—
888C23—361no—
889C23C22×(C3⋊D3)⋊C311yescharacteristic
890C23C22×(C3⋊D3)⋊C311yescharacteristic
891C23C22×(C3⋊D3)⋊C311yescharacteristic
892Q8—182no—
893D4—94no—
894D4—182no—
895D4—182no—
896D4—182no—
897D4—182no—
898D4—182no—
899D4—182no—
900D4—361no—
901D4—361no—
902C2×C4—22no—
903C2×C4—41no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—91no—
909C2×C4—182no—
910C2×C4—182no—
911C2×C4—182no—
912C2×C4—361no—
913C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
914C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
915C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
916C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
917C2×C3—22no—
918C2×C3—22no—
919C2×C3—31no—
920C2×C3—31no—
921C2×C3—31no—
922C2×C3—31no—
923C2×C3—31no—
924C2×C3—31no—
925C2×C3—41no—
926C2×C3—62no—
927C2×C3—62no—
928C2×C3—62no—
929C2×C3—62no—
930C2×C3—64no—
931C2×C3—61no—
932C2×C3—61no—
933C2×C3—61no—
934C2×C3—122no—
935C2×C3—121no—
936C2×C3—121no—
937C2×C3—122no—
938C2×C3—182no—
939C2×C3—361no—
940C2×C3—361no—
941C2×C3C2×C3×#23511yescharacteristic
942C2×C3C2×C3×D3×D411yescharacteristic
943C2×C3C3×#100411yescharacteristic
944D3—62no—
945D3—121no—
946D3—121no—
947D3—182no—
948D3—361no—
949D3—361no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—44no—
958C22—92no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—364no—
968C22#3828⋊C312yescomplemented
969C22D4×(C3⋊D3)⋊C312yes—
970C22C23×(C3⋊D3)⋊C311yescharacteristic
971C4—21no—
972C4—21no—
973C4—21no—
974C4—21no—
975C4—92no—
976C4—181no—
977C4—181no—
978C4—181no—
979C4—181no—
980C3—31no—
981C3—31no—
982C3—61no—
983C3C3×#549011yescharacteristic
984C2—22no—
985C2—22no—
986C2—41no—
987C2—182no—
988C2—361no—
989C2—361no—
990C2C2×#3828⋊C311yescharacteristic
991C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
992C2#64361⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#638⋊C3C2semidirect
2. C2×#3828⋊C3C2semidirect
3. C2×C22⋊C4×H(3,𝔽3)C2semidirect
4. #11721702C2semidirect
5. #64139⋊C3C2semidirect
6. #64138⋊C3C2semidirect
7. C4×#638⋊C3C2semidirect
8. #64094⋊C3C2semidirect
9. #64093⋊C3C2semidirect
10. #64093⋊C3C2semidirect
11. #64092⋊C3C2semidirect
12. #64091⋊C3C2semidirect
13. #64090⋊C3C2semidirect
14. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
15. #64087⋊C3C2semidirect
16. #10595961C3semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
21. C22×C4×H(3,𝔽3)C22semidirect
28. C2×#638⋊C3C22semidirect
29. C2×#638⋊C3C22semidirect
32. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
33. 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
40. C22⋊C4×H(3,𝔽3)C22semidirect
41. C22⋊C4×H(3,𝔽3)C22semidirect
43. #3757⋊C3C22semidirect
44. #3757⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3752⋊C3C22semidirect
47. #3752⋊C3C22semidirect
48. #3752⋊C3C22semidirect
49. #3752⋊C3C22semidirect
50. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
51. #3750⋊C3C22semidirect
52. #3750⋊C3C22semidirect
53. #3750⋊C3C22semidirect
54. C4×(C3⋊Dic3)⋊C3C22semidirect
55. C22×#638C2×C3semidirect
56. C2×#3828C2×C3semidirect
60. C2×C32×C22⋊C4D3semidirect
61. C2×C32×C22⋊C4C2×C3semidirect
62. #64162C2×C3semidirect
63. #64139C2×C3semidirect
64. #64138C2×C3semidirect
65. C4×#638C2×C3semidirect
66. #64094C2×C3semidirect
67. #64093C2×C3semidirect
68. #64093C2×C3semidirect
69. #64092C2×C3semidirect
70. #64091C2×C3semidirect
71. #64090C2×C3semidirect
72. C22⋊C4×C3⋊D3C2×C3semidirect
73. #64087C2×C3semidirect
110. #638⋊C3D4semidirect
133. C22×C32×C4C2×D3semidirect
134. C22×C32×C4C2×D3semidirect
135. C22×C32×C4C22×C3semidirect
136. C22×C32×C4C22×C3semidirect
143. C2×#638C22×C3semidirect
144. C2×#638C22×C3semidirect
147. C2×C4⋊(C3⋊D3)C22×C3semidirect
148. C2×C4⋊(C3⋊D3)C22×C3semidirect
149. C2×C4×C3⋊D3C22×C3semidirect
150. C2×C4×C3⋊D3C22×C3semidirect
151. C2×C4×C3⋊D3C22×C3semidirect
152. C2×#634C22×C3semidirect
175. C32×C22⋊C4C2×D3semidirect
176. C32×C22⋊C4C2×D3semidirect
179. C32×C22⋊C4C22×C3semidirect
180. C32×C22⋊C4C22×C3semidirect
182. #3757C22×C3semidirect
183. #3757C22×C3semidirect
184. #3752C22×C3semidirect
185. #3752C22×C3semidirect
186. #3752C22×C3semidirect
187. #3752C22×C3semidirect
188. #3752C22×C3semidirect
189. C4⋊(C3⋊Dic3)C22×C3semidirect
190. #3750C22×C3semidirect
191. #3750C22×C3semidirect
192. #3750C22×C3semidirect
193. C4×C3⋊Dic3C22×C3semidirect
216. C22×H(3,𝔽3)#41semidirect
337. #638C3×D4semidirect
524. C22×C32#235semidirect
527. C22×C32C3×#41semidirect
586. C2×C22⋊C4(C3⋊D3)⋊C3semidirect
587. H(3,𝔽3)#546semidirect
753. C22×C4C2×(C3⋊D3)⋊C3semidirect
754. C22×C4C2×(C3⋊D3)⋊C3semidirect
769. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
770. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
878. C32#5490semidirect
879. C32C3×#546semidirect
968. C22#3828⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C2×#3828⋊C32
C2×C22⋊C4×H(3,𝔽3)2
#117217022
#64139⋊C32
#64138⋊C32
C4×#638⋊C32
#64094⋊C32
#64093⋊C32
#64092⋊C32
#64091⋊C32
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#105959613
C3×#54903