Finite Group Databasebeta

← #10596134⋊C3 #13153040

Subgroups — #10596134⋊C3 #13153040

Order 1728.

918 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
2#64149⋊C3C211yesmaximal, characteristic, complemented
3#64148⋊C3C211yesmaximal, characteristic, complemented
4#64139⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#64104⋊C3C211yesmaximal, characteristic, complemented
7#64103⋊C3C211yesmaximal, characteristic, complemented
8#64101⋊C3C211yesmaximal, characteristic, complemented
9#64098⋊C3C211yesmaximal, characteristic, complemented
10#64095⋊C3C211yesmaximal, characteristic, complemented
11#64093⋊C3C211yesmaximal, characteristic, complemented
12#64093⋊C3C211yesmaximal, characteristic, complemented
13#64093⋊C3C211yesmaximal, characteristic, complemented
14#64092⋊C3C211yesmaximal, characteristic, complemented
15#64090⋊C3C211yesmaximal, characteristic, complemented
16#10596134C311yesmaximal, characteristic, complemented
17C3×#5663—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C2×#638⋊C3C2211yescharacteristic
26C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
27C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
29C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
30C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
31C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
32C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
33C4⋊C4×H(3,𝔽3)C2211yescharacteristic
34C4⋊C4×H(3,𝔽3)C2211yescharacteristic
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic
36C22⋊C4×H(3,𝔽3)C2211yescharacteristic
37C22⋊C4×H(3,𝔽3)C2211yescharacteristic
38#3757⋊C3C2211yescharacteristic
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
47#3750⋊C3C2211yescharacteristic
48#3750⋊C3C2211yescharacteristic
49#3750⋊C3C2211yescharacteristic
50#3750⋊C3C2211yescharacteristic
51C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
52C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
53C32×#123—21no—
54C32×#123D311yescharacteristic, complemented
55C32×#123C2×C311yescharacteristic, complemented
56#64149C2×C311yescharacteristic, complemented
57#64148C2×C311yescharacteristic, complemented
58#64139C2×C311yescharacteristic, complemented
59C4×#638C2×C311yescharacteristic, complemented
60#64104C2×C311yescharacteristic, complemented
61#64103C2×C311yescharacteristic, complemented
62#64101C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64095C2×C311yescharacteristic, complemented
65#64093C2×C311yescharacteristic, complemented
66#64093C2×C311yescharacteristic, complemented
67#64093C2×C311yescharacteristic, complemented
68#64092C2×C311yescharacteristic, complemented
69#64090C2×C311yescharacteristic, complemented
70C3×#940—31no—
71C3×#939—31no—
72C3×#930—31no—
73C3×C4×#67—31no—
74C3×#895—31no—
75C3×#894—31no—
76C3×#892—31no—
77C3×#889—31no—
78C3×#886—31no—
79C3×#884—31no—
80C3×#884—31no—
81C3×#884—31no—
82C3×#883—31no—
83C3×#67⋊C4—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89D4×H(3,𝔽3)—41no—
90C2×C4×H(3,𝔽3)—41no—
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×C4×H(3,𝔽3)C2311yescharacteristic
95C2×C4×H(3,𝔽3)C2311yescharacteristic
96#638⋊C3—22no—
97#638⋊C3—22no—
98#638⋊C3—41no—
99#638⋊C3—41no—
100#638⋊C3—41no—
101#638⋊C3—41no—
102C2×(C3⋊Dic3)⋊C3—41no—
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C4⋊((C3⋊D3)⋊C3)—41no—
109C4⋊((C3⋊D3)⋊C3)—41no—
110C4⋊((C3⋊D3)⋊C3)—41no—
111C4×(C3⋊D3)⋊C3—22no—
112C4×(C3⋊D3)⋊C3—41no—
113C4×(C3⋊D3)⋊C3—41no—
114C3×#540—91no—
115#5663—31no—
116#5663—91no—
117C2×C32×D4—21no—
118C2×C32×D4C2×D311yescharacteristic
119C2×C32×D4C22×C311yescharacteristic
120C22×C32×C4—21no—
121C22×C32×C4C2×D311yescharacteristic
122C22×C32×C4C22×C311yescharacteristic
123C2×#638C22×C311yescharacteristic
124C2×#638C22×C311yescharacteristic
125C2×#638C22×C311yescharacteristic
126C2×#638C22×C311yescharacteristic
127C2×#638C22×C311yescharacteristic
128C2×#638C22×C311yescharacteristic
129C22×C3⋊Dic3C22×C311yescharacteristic
130C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
131C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
132C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
133C2×C4×C3⋊D3C22×C311yescharacteristic
134C2×C4×C3⋊D3C22×C311yescharacteristic
135C2×C4×C3⋊D3C22×C311yescharacteristic
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C22×C3×Dic3—31no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C32×C4⋊C4—21no—
150C32×C4⋊C4—21no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C22×C311yescharacteristic
154C32×C4⋊C4C22×C311yescharacteristic
155C32×C22⋊C4—21no—
156C32×C22⋊C4—21no—
157C32×C22⋊C4—21no—
158C32×C22⋊C4C2×D311yescharacteristic
159C32×C22⋊C4C2×D311yescharacteristic
160C32×C22⋊C4C2×D311yescharacteristic
161C32×C22⋊C4C22×C311yescharacteristic
162C32×C22⋊C4C22×C311yescharacteristic
163C32×C22⋊C4C22×C311yescharacteristic
164#3757C22×C311yescharacteristic
165#3752C22×C311yescharacteristic
166#3752C22×C311yescharacteristic
167#3752C22×C311yescharacteristic
168#3752C22×C311yescharacteristic
169#3752C22×C311yescharacteristic
170#3752C22×C311yescharacteristic
171C4⋊(C3⋊Dic3)C22×C311yescharacteristic
172C4⋊(C3⋊Dic3)C22×C311yescharacteristic
173#3750C22×C311yescharacteristic
174#3750C22×C311yescharacteristic
175#3750C22×C311yescharacteristic
176#3750C22×C311yescharacteristic
177C4×C3⋊Dic3C22×C311yescharacteristic
178C4×C3⋊Dic3C22×C311yescharacteristic
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×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×C4×Dic3—31no—
193C3×C4×Dic3—31no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)—21no—
197C22×H(3,𝔽3)—21no—
198C22×H(3,𝔽3)—21no—
199C22×H(3,𝔽3)—21no—
200C22×H(3,𝔽3)C2411yescharacteristic
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—21no—
210C4×H(3,𝔽3)—21no—
211C4×H(3,𝔽3)—21no—
212C4×H(3,𝔽3)—21no—
213C4×H(3,𝔽3)—21no—
214C4×H(3,𝔽3)—21no—
215(C3⋊Dic3)⋊C3—21no—
216(C3⋊Dic3)⋊C3—21no—
217(C3⋊Dic3)⋊C3—21no—
218(C3⋊Dic3)⋊C3—21no—
219(C3⋊Dic3)⋊C3#4112yes—
220C3×#127—91no—
221C3×#125—91no—
222C3×#123—31no—
223C3×#123—31no—
224C3×#123—61no—
225C3×#123—91no—
226C3×#123—91no—
227C3×#123—91no—
228C3×#123C3×D311yescharacteristic
229C3×#121—91no—
230C3×#121—91no—
231C3×#121—91no—
232C3×#121—91no—
233C3×#121—91no—
234C3×#121—91no—
235C3×C4×D4—91no—
236C3×C4×D4—91no—
237C3×#117—91no—
238#940—31no—
239#940—91no—
240#939—31no—
241#939—91no—
242#930—31no—
243#930—91no—
244C4×#67—31no—
245C4×#67—91no—
246#895—31no—
247#895—91no—
248#894—31no—
249#894—91no—
250#892—31no—
251#892—91no—
252#889—31no—
253#889—91no—
254#886—31no—
255#886—91no—
256#884—31no—
257#884—31no—
258#884—31no—
259#884—91no—
260#884—91no—
261#884—91no—
262#883—31no—
263#883—91no—
264#67⋊C4—31no—
265#67⋊C4—91no—
266C23×C32—21no—
267C23×C32—21no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C23×C32C23×C311yescharacteristic
271C23×C32C23×C311yescharacteristic
272C22×C3⋊D3C23×C311yescharacteristic
273C22×C3⋊D3C23×C311yescharacteristic
274C22×C3⋊D3C23×C311yescharacteristic
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C32×D4—41no—
279C32×D4—41no—
280C32×D4—42no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—41no—
287C2×C32×C4—41no—
288C2×C32×C4—42no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295C2×C32×C4C23×C311yescharacteristic
296C2×C32×C4C23×C311yescharacteristic
297C2×C32×C4C23×C311yescharacteristic
298C2×C32×C4C23×C311yescharacteristic
299#638—22no—
300#638—22no—
301#638—41no—
302#638—41no—
303#638—41no—
304#638—41no—
305C2×C3⋊Dic3—41no—
306C2×C3⋊Dic3C23×C311yescharacteristic
307C2×C3⋊Dic3C23×C311yescharacteristic
308C2×C3⋊Dic3C23×C311yescharacteristic
309C2×C3⋊Dic3C23×C311yescharacteristic
310C2×C3⋊Dic3C23×C311yescharacteristic
311C4⋊(C3⋊D3)—41no—
312C4⋊(C3⋊D3)—41no—
313C4⋊(C3⋊D3)—41no—
314C4×C3⋊D3—22no—
315C4×C3⋊D3—41no—
316C4×C3⋊D3—41no—
317C3×#67—62no—
318C3×#67—62no—
319C3×#67—121no—
320C3×#67—121no—
321C3×#67—121no—
322C3×#67—121no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—121no—
329C3×D12—121no—
330C3×D12—121no—
331C3×D12—121no—
332C3×C4×D3—62no—
333C3×C4×D3—121no—
334C3×C4×D3—121no—
335#540—91noSylow
336C2×H(3,𝔽3)—41no—
337C2×H(3,𝔽3)—41no—
338C2×H(3,𝔽3)C2×#4111yescharacteristic
339C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
340C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
341(C3⋊D3)⋊C3—41no—
342(C3⋊D3)⋊C3—41no—
343(C3⋊D3)⋊C3—41no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—61no—
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—
354C2×C3×D4—91no—
355C2×C3×D4—91no—
356C2×C3×D4C2×C3×D311yescharacteristic
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—61no—
360C22×C3×C4—91no—
361C22×C3×C4—91no—
362C22×C3×C4—91no—
363C22×C3×C4—91no—
364C22×C3×C4C2×C3×D311yescharacteristic
365C2×#67—31no—
366C2×#67—31no—
367C2×#67—31no—
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—31no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C22×Dic3—31no—
378C22×Dic3—91no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—91no—
383C2×D12—91no—
384C2×D12—91no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—31no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—91no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4—91no—
398C3×C4⋊C4—91no—
399C3×C4⋊C4—91no—
400C3×C4⋊C4—91no—
401C3×C4⋊C4—91no—
402C3×C4⋊C4—91no—
403C3×C4⋊C4C2×C3×D311yescharacteristic
404C3×C4⋊C4C2×C3×D311yescharacteristic
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4C2×C3×D311yescharacteristic
422C3×C22⋊C4C2×C3×D311yescharacteristic
423C3×C22⋊C4C2×C3×D311yescharacteristic
424C3×C42—91no—
425C3×C42—91no—
426#217—31no—
427#217—91no—
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—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444Dic3⋊C4—31no—
445Dic3⋊C4—31no—
446Dic3⋊C4—31no—
447Dic3⋊C4—31no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C22×C32—22no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32C23×D311yescharacteristic
476C22×C32C24×C311yescharacteristic
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
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—61no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
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—
510C3⋊Dic3—21no—
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—21no—
514C3⋊Dic3C3×#4112yes—
515C3×Dic3—32no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520#127—91no—
521#125—91no—
522#123—91no—
523#123—91no—
524#123—91no—
525#123(C3⋊D3)⋊C311yescharacteristic, complemented
526#121—91no—
527#121—91no—
528#121—91no—
529#121—91no—
530#121—91no—
531#121—91no—
532C4×D4—91no—
533C4×D4—91no—
534#117—91no—
535H(3,𝔽3)#54011yescharacteristic, complemented, Sylow
536C23×C3—31no—
537C23×C3—31no—
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—91no—
543C23×C3—91no—
544C23×C3—91no—
545C23×C3C22×C3×D311yescharacteristic
546C23×C3C22×C3×D311yescharacteristic
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—91no—
551C22×D3—91no—
552C22×D3—91no—
553C3×D4—41no—
554C3×D4—121no—
555C3×D4—121no—
556C3×D4—122no—
557C3×D4—182no—
558C3×D4—182no—
559C3×D4—361no—
560C3×D4—361no—
561C3×D4—361no—
562C3×D4—361no—
563C3×D4—361no—
564C3×D4—361no—
565C3×D4—361no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
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—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—91no—
585C2×C3×C4—91no—
586C2×C3×C4—91no—
587C2×C3×C4—121no—
588C2×C3×C4—121no—
589C2×C3×C4—122no—
590C2×C3×C4—182no—
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
599#67—62no—
600#67—62no—
601#67—121no—
602#67—121no—
603#67—121no—
604#67—121no—
605#67—182no—
606#67—182no—
607#67—361no—
608#67—361no—
609#67—361no—
610#67—361no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—91no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—121no—
622C2×Dic3—361no—
623D12—121no—
624D12—121no—
625D12—121no—
626D12—361no—
627D12—361no—
628D12—361no—
629C4×D3—62no—
630C4×D3—121no—
631C4×D3—121no—
632C4×D3—182no—
633C4×D3—361no—
634C4×D3—361no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—42no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—41no—
642C2×C32—41no—
643C2×C32—81no—
644C2×C32#100411yescharacteristic
645C2×C32D3×#4111yescharacteristic
646C2×C32#100911yescharacteristic
647C2×C32C2×C3×#4111yescharacteristic
648C2×C32C3×H(5,𝔽2)11yescharacteristic
649C2×C32C3×H(5,𝔽2)11yescharacteristic
650C3⋊D3—41no—
651C3⋊D3—41no—
652C3⋊D3—41no—
653C3×D3—121no—
654C3×D3—121no—
655C3×D3—121no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—91no—
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—91no—
665C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
671C4⋊C4—91no—
672C4⋊C4—91no—
673C4⋊C4—91no—
674C4⋊C4—91no—
675C4⋊C4—91no—
676C4⋊C4—91no—
677C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
678C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4—91no—
683C22⋊C4—91no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
687C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
688C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
689C42—91no—
690C42—91no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—31no—
698C22×C3—31no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—61no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3C23×C3×D311yescharacteristic
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3—181no—
741C2×D3—181no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
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—61no—
761C3×C4—92no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4—181no—
768C3×C4—181no—
769C3×C4—181no—
770C3×C4—181no—
771Dic3—32no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—92no—
777Dic3—181no—
778Dic3—181no—
779Dic3—181no—
780Dic3—181no—
781C32—21no—
782C32#566311yescharacteristic, complemented
783C32C3×#54011yescharacteristic, complemented
784C23—91no—
785C23—91no—
786C23—91no—
787C23C22×(C3⋊D3)⋊C311yescharacteristic
788C23C22×(C3⋊D3)⋊C311yescharacteristic
789D4—41no—
790D4—182no—
791D4—182no—
792D4—361no—
793D4—361no—
794D4—361no—
795D4—361no—
796D4—361no—
797D4—361no—
798D4—361no—
799C2×C4—41no—
800C2×C4—91no—
801C2×C4—91no—
802C2×C4—91no—
803C2×C4—91no—
804C2×C4—91no—
805C2×C4—182no—
806C2×C4—361no—
807C2×C4—361no—
808C2×C4—361no—
809C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
810C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
811C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
812C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
813C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
814C2×C3—31no—
815C2×C3—31no—
816C2×C3—31no—
817C2×C3—31no—
818C2×C3—31no—
819C2×C3—31no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—61no—
823C2×C3—61no—
824C2×C3—61no—
825C2×C3—121no—
826C2×C3—121no—
827C2×C3—121no—
828C2×C3—121no—
829C2×C3—122no—
830C2×C3—241no—
831C2×C3—361no—
832C2×C3—361no—
833C2×C3—361no—
834C2×C3C3×#100411yescharacteristic
835C2×C3C3×D3×#4111yescharacteristic
836C2×C3C3×#100911yescharacteristic
837D3—121no—
838D3—121no—
839D3—121no—
840D3—361no—
841D3—361no—
842D3—361no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—181no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22C23×(C3⋊D3)⋊C311yescharacteristic
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—92no—
865C4—181no—
866C4—181no—
867C4—181no—
868C4—181no—
869C3—31no—
870C3—31no—
871C3—61no—
872C3C3×#566311yescharacteristic
873C2—41no—
874C2—41no—
875C2—361no—
876C2—361no—
877C2—361no—
878C2#64361⋊C311yescharacteristic
879C2#41×(C3⋊D3)⋊C311yescharacteristic
880C2#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×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. H(3,𝔽3)×#123C2semidirect
2. #64149⋊C3C2semidirect
3. #64148⋊C3C2semidirect
4. #64139⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #64104⋊C3C2semidirect
7. #64103⋊C3C2semidirect
8. #64101⋊C3C2semidirect
9. #64098⋊C3C2semidirect
10. #64095⋊C3C2semidirect
11. #64093⋊C3C2semidirect
12. #64093⋊C3C2semidirect
13. #64093⋊C3C2semidirect
14. #64092⋊C3C2semidirect
15. #64090⋊C3C2semidirect
16. #10596134C3semidirect
54. C32×#123D3semidirect
55. C32×#123C2×C3semidirect
56. #64149C2×C3semidirect
57. #64148C2×C3semidirect
58. #64139C2×C3semidirect
59. C4×#638C2×C3semidirect
60. #64104C2×C3semidirect
61. #64103C2×C3semidirect
62. #64101C2×C3semidirect
63. #64098C2×C3semidirect
64. #64095C2×C3semidirect
65. #64093C2×C3semidirect
66. #64093C2×C3semidirect
67. #64093C2×C3semidirect
68. #64092C2×C3semidirect
69. #64090C2×C3semidirect
525. #123(C3⋊D3)⋊C3semidirect
535. H(3,𝔽3)#540semidirect
782. C32#5663semidirect
783. C32C3×#540semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1232
#64149⋊C32
#64148⋊C32
#64139⋊C32
C4×#638⋊C32
#64104⋊C32
#64103⋊C32
#64101⋊C32
#64098⋊C32
#64095⋊C32
#64093⋊C32
#64092⋊C32
#64090⋊C32
#105961343
C3×#56633