Finite Group Databasebeta

← #10596136⋊C3 #13153052

Subgroups — #10596136⋊C3 #13153052

Order 1728.

841 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
2#64148⋊C3C211yesmaximal, characteristic
3D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4#64138⋊C3C211yesmaximal, characteristic, complemented
5C2×C4⋊((C3⋊Dic3)⋊C3)C211yesmaximal, characteristic, complemented
6#64107⋊C3C211yesmaximal, characteristic, complemented
7#64106⋊C3C211yesmaximal, characteristic, complemented
8#64099⋊C3C211yesmaximal, characteristic, complemented
9#64098⋊C3C211yesmaximal, characteristic, complemented
10#64095⋊C3C211yesmaximal, characteristic, complemented
11#64092⋊C3C211yesmaximal, characteristic, complemented
12#64090⋊C3C211yesmaximal, characteristic, complemented
13#64088⋊C3C211yesmaximal, characteristic, complemented
14#64087⋊C3C211yesmaximal, characteristic, complemented
15#64087⋊C3C211yesmaximal, characteristic, complemented
16#10596136C311yesmaximal, characteristic, complemented
17C3×#5665—31nomaximal
18C2×D4×H(3,𝔽3)C2211yescharacteristic
19C22×C4×H(3,𝔽3)C2211yescharacteristic
20C2×#638⋊C3C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#634⋊C3C2211yescharacteristic
27C4⋊C4×H(3,𝔽3)C2211yescharacteristic
28C4⋊C4×H(3,𝔽3)C2211yescharacteristic
29C22⋊C4×H(3,𝔽3)C2211yescharacteristic
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic
39C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
40C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
41C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
42C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
43C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic
45#3750⋊C3C2211yescharacteristic
46#3750⋊C3C2211yescharacteristic
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#64148C2×C311yescharacteristic
57D4×C3⋊Dic3C2×C311yescharacteristic, complemented
58#64138C2×C311yescharacteristic, complemented
59C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic, complemented
60#64107C2×C311yescharacteristic, complemented
61#64106C2×C311yescharacteristic, complemented
62#64099C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64095C2×C311yescharacteristic, complemented
65#64092C2×C311yescharacteristic, complemented
66#64090C2×C311yescharacteristic, complemented
67#64088C2×C311yescharacteristic, complemented
68#64087C2×C311yescharacteristic, complemented
69#64087C2×C311yescharacteristic, complemented
70C3×#939—31no—
71C3×D4×Dic3—31no—
72C3×#929—31no—
73C2×C3×C4⋊Dic3—31no—
74C3×#898—31no—
75C3×#897—31no—
76C3×#890—31no—
77C3×#889—31no—
78C3×#886—31no—
79C3×#883—31no—
80C3×#67⋊C4—31no—
81C3×#879—31no—
82C3×#878—31no—
83C3×#878—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87D4×H(3,𝔽3)—22no—
88C2×C4×H(3,𝔽3)—22no—
89C2×C4×H(3,𝔽3)C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94#638⋊C3—22no—
95#638⋊C3—41no—
96C2×(C3⋊Dic3)⋊C3—41no—
97C2×(C3⋊Dic3)⋊C3—41no—
98C2×(C3⋊Dic3)⋊C3—41no—
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C4×(C3⋊D3)⋊C3—41no—
107#634⋊C3—41no—
108C3×#539—91no—
109#5665—31no—
110#5665—91no—
111C2×C32×D4—21no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C22×C311yescharacteristic
114C22×C32×C4—21no—
115C22×C32×C4C2×D311yescharacteristic
116C22×C32×C4C22×C311yescharacteristic
117C2×#638C22×C311yescharacteristic
118C2×#638C22×C311yescharacteristic
119C22×C3⋊Dic3C22×C311yescharacteristic
120C22×C3⋊Dic3C22×C311yescharacteristic
121C22×C3⋊Dic3C22×C311yescharacteristic
122C2×C4×C3⋊D3C22×C311yescharacteristic
123C2×#634C22×C311yescharacteristic
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—31no—
129C2×C3×C4×D3—31no—
130C2×C3×Dic6—31no—
131C32×C4⋊C4—21no—
132C32×C4⋊C4—21no—
133C32×C4⋊C4C2×D311yescharacteristic
134C32×C4⋊C4C2×D311yescharacteristic
135C32×C4⋊C4C22×C311yescharacteristic
136C32×C4⋊C4C22×C311yescharacteristic
137C32×C22⋊C4—21no—
138C32×C22⋊C4—21no—
139C32×C22⋊C4—21no—
140C32×C22⋊C4C2×D311yescharacteristic
141C32×C22⋊C4C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C22×C311yescharacteristic
144C32×C22⋊C4C22×C311yescharacteristic
145C32×C22⋊C4C22×C311yescharacteristic
146#3757C22×C311yescharacteristic
147#3757C22×C311yescharacteristic
148#3757C22×C311yescharacteristic
149#3752C22×C311yescharacteristic
150#3752C22×C311yescharacteristic
151#3752C22×C311yescharacteristic
152#3752C22×C311yescharacteristic
153C4⋊(C3⋊Dic3)C22×C311yescharacteristic
154C4⋊(C3⋊Dic3)C22×C311yescharacteristic
155C4⋊(C3⋊Dic3)C22×C311yescharacteristic
156C4⋊(C3⋊Dic3)C22×C311yescharacteristic
157C4⋊(C3⋊Dic3)C22×C311yescharacteristic
158C4⋊(C3⋊Dic3)C22×C311yescharacteristic
159#3750C22×C311yescharacteristic
160#3750C22×C311yescharacteristic
161#3750C22×C311yescharacteristic
162#3750C22×C311yescharacteristic
163#3750C22×C311yescharacteristic
164#3750C22×C311yescharacteristic
165C4×C3⋊Dic3C22×C311yescharacteristic
166C4×C3⋊Dic3C22×C311yescharacteristic
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×C4×Dic3—31no—
187C3×C4×Dic3—31no—
188C22×H(3,𝔽3)—21no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)#4112yes—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
198C4×H(3,𝔽3)—21no—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)—21no—
201C4×H(3,𝔽3)—21no—
202C4×H(3,𝔽3)—21no—
203(C3⋊Dic3)⋊C3—21no—
204(C3⋊Dic3)⋊C3—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3—21no—
210C3×#126—91no—
211C3×#126—91no—
212C3×#125—91no—
213C3×#125—91no—
214C3×#123—31no—
215C3×#123—31no—
216C3×#123—61no—
217C3×#123—91no—
218C3×#123—91no—
219C3×#123—91no—
220C3×#123C3×D311yescharacteristic
221C3×C22⋊Q8—91no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8—91no—
224C3×#121—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C2×C3×C4⋊C4—91no—
228#939—31no—
229#939—91no—
230D4×Dic3—31no—
231D4×Dic3—91no—
232#929—31no—
233#929—91no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—91no—
236#898—31no—
237#898—91no—
238#897—31no—
239#897—91no—
240#890—31no—
241#890—91no—
242#889—31no—
243#889—91no—
244#886—31no—
245#886—91no—
246#883—31no—
247#883—91no—
248#67⋊C4—31no—
249#67⋊C4—91no—
250#879—31no—
251#879—91no—
252#878—31no—
253#878—31no—
254#878—91no—
255#878—91no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32C22×D311yescharacteristic
259C23×C32C22×D311yescharacteristic
260C23×C32C23×C311yescharacteristic
261C23×C32C23×C311yescharacteristic
262C22×C3⋊D3C23×C311yescharacteristic
263C22×C3×D3—31no—
264C32×D4—22no—
265C32×D4—22no—
266C32×D4—42no—
267C2×C32×C4—22no—
268C2×C32×C4—22no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C23×C311yescharacteristic
281C2×C32×C4C23×C311yescharacteristic
282C2×C32×C4C23×C311yescharacteristic
283C2×C32×C4C23×C311yescharacteristic
284C2×C32×C4C23×C311yescharacteristic
285#638—22no—
286#638—41no—
287C2×C3⋊Dic3—41no—
288C2×C3⋊Dic3—41no—
289C2×C3⋊Dic3—41no—
290C2×C3⋊Dic3C23×C311yescharacteristic
291C2×C3⋊Dic3C23×C311yescharacteristic
292C2×C3⋊Dic3C23×C311yescharacteristic
293C2×C3⋊Dic3C23×C311yescharacteristic
294C2×C3⋊Dic3C23×C311yescharacteristic
295C2×C3⋊Dic3C23×C311yescharacteristic
296C2×C3⋊Dic3C23×C311yescharacteristic
297C4×C3⋊D3—41no—
298#634—41no—
299C3×#67—62no—
300C3×#67—121no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—121no—
309C2×C3×Dic3—121no—
310C2×C3×Dic3—121no—
311C3×C4×D3—121no—
312C3×Dic6—121no—
313#539—91noSylow
314C2×H(3,𝔽3)—22no—
315C2×H(3,𝔽3)—41no—
316C2×H(3,𝔽3)C2×#4111yescharacteristic
317C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
318C2×H(3,𝔽3)2−1+411yescharacteristic
319(C3⋊D3)⋊C3—41no—
320C2×C3×Q8—91no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—91no—
325C2×C3×D4—91no—
326C2×C3×D4C2×C3×D311yescharacteristic
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—91no—
331C22×C3×C4—91no—
332C22×C3×C4—91no—
333C22×C3×C4—91no—
334C22×C3×C4C2×C3×D311yescharacteristic
335C2×#67—31no—
336C2×#67—31no—
337C2×#67—91no—
338C2×#67—91no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345C2×C4×D3—31no—
346C2×C4×D3—91no—
347C2×Dic6—31no—
348C2×Dic6—91no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—91no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4C2×C3×D311yescharacteristic
368C3×C4⋊C4C2×C3×D311yescharacteristic
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4C2×C3×D311yescharacteristic
386C3×C22⋊C4C2×C3×D311yescharacteristic
387C3×C22⋊C4C2×C3×D311yescharacteristic
388C3×C42—91no—
389C3×C42—91no—
390#217—31no—
391#217—31no—
392#217—31no—
393#217—91no—
394#217—91no—
395#217—91no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404C4⋊Dic3—31no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—31no—
410C4⋊Dic3—91no—
411C4⋊Dic3—91no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—31no—
419Dic3⋊C4—31no—
420Dic3⋊C4—31no—
421Dic3⋊C4—31no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—21no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—22no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32#23712yes—
450C22×C32C3×#4112yes—
451C22×C32C23×D311yescharacteristic
452C22×C32C24×C311yescharacteristic
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3—21no—
456C2×C3×D3—61no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—21no—
464C32×C4—21no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4—41no—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—61no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488#126—91no—
489#126—91no—
490#125—91no—
491#125—91no—
492#123—91no—
493#123—91no—
494#123—91no—
495#123(C3⋊D3)⋊C311yescharacteristic, complemented
496C22⋊Q8—91no—
497C22⋊Q8—91no—
498C22⋊Q8—91no—
499#121—91no—
500C4×D4—91no—
501C4×D4—91no—
502C2×C4⋊C4—91no—
503H(3,𝔽3)#53911yescharacteristic, complemented, Sylow
504C23×C3—31no—
505C23×C3—31no—
506C23×C3—31no—
507C23×C3—31no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3—91no—
511C23×C3C22×C3×D311yescharacteristic
512C23×C3C22×C3×D311yescharacteristic
513C22×D3—31no—
514C22×D3—91no—
515C3×Q8—361no—
516C3×D4—22no—
517C3×D4—62no—
518C3×D4—62no—
519C3×D4—122no—
520C3×D4—182no—
521C3×D4—361no—
522C2×C3×C4—22no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—62no—
534C2×C3×C4—62no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—122no—
548C2×C3×C4—361no—
549C2×C3×C4—361no—
550C2×C3×C4—361no—
551C2×C3×C4—361no—
552C2×C3×C4C22×C3×D311yescharacteristic
553C2×C3×C4C22×C3×D311yescharacteristic
554C2×C3×C4C22×C3×D311yescharacteristic
555C2×C3×C4C22×C3×D311yescharacteristic
556C2×C3×C4C22×C3×D311yescharacteristic
557#67—62no—
558#67—121no—
559#67—182no—
560#67—361no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—91no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3—361no—
579C2×Dic3—361no—
580C2×Dic3—361no—
581C4×D3—121no—
582C4×D3—361no—
583Dic6—121no—
584Dic6—361no—
585C2×C32—22no—
586C2×C32—22no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—42no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—81no—
594C2×C32C2×#23711yescharacteristic
595C2×C32#100911yescharacteristic
596C2×C32#101011yescharacteristic
597C2×C32C2×C3×#4111yescharacteristic
598C2×C32C3×H(5,𝔽2)11yescharacteristic
599C2×C32C3×2−1+411yescharacteristic
600C3⋊D3—41no—
601C3×D3—121no—
602C2×Q8—91no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—91no—
609C22×C4—91no—
610C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
624C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
633C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
634C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
635C42—91no—
636C42—91no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—31no—
643C22×C3—31no—
644C22×C3—32no—
645C22×C3—32no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—62no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3C3×#23712yes—
667C22×C3C23×C3×D311yescharacteristic
668C2×D3—61no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697C3×C4—181no—
698C3×C4—181no—
699C3×C4—181no—
700C3×C4—181no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—61no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—181no—
714Dic3—181no—
715C32—21no—
716C32#566511yescharacteristic, complemented
717C32C3×#53911yescharacteristic, complemented
718C23—91no—
719C23C22×(C3⋊D3)⋊C311yescharacteristic
720C23C22×(C3⋊D3)⋊C311yescharacteristic
721Q8—361no—
722D4—22no—
723D4—182no—
724D4—361no—
725C2×C4—22no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—361no—
734C2×C4—361no—
735C2×C4—361no—
736C2×C4—361no—
737C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
738C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
739C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
740C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
741C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
742C2×C3—22no—
743C2×C3—31no—
744C2×C3—31no—
745C2×C3—31no—
746C2×C3—31no—
747C2×C3—31no—
748C2×C3—31no—
749C2×C3—41no—
750C2×C3—62no—
751C2×C3—62no—
752C2×C3—61no—
753C2×C3—61no—
754C2×C3—61no—
755C2×C3—122no—
756C2×C3—121no—
757C2×C3—121no—
758C2×C3—241no—
759C2×C3—361no—
760C2×C3C2×C3×#23711yescharacteristic
761C2×C3C3×#100911yescharacteristic
762C2×C3C3×#101011yescharacteristic
763D3—121no—
764D3—361no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22#3830⋊C312yes—
774C22C23×(C3⋊D3)⋊C311yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—21no—
780C4—181no—
781C4—181no—
782C4—181no—
783C4—181no—
784C4—181no—
785C4—181no—
786C4—181no—
787C3—31no—
788C3—31no—
789C3—61no—
790C3C3×#566511yescharacteristic
791C2—22no—
792C2—41no—
793C2—361no—
794C2C2×#3830⋊C311yescharacteristic
795C2#1172263811yescharacteristic
796C2#1172263911yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
prime radical#64148⋊C3C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#539
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
3. D4×(C3⋊Dic3)⋊C3C2semidirect
4. #64138⋊C3C2semidirect
5. C2×C4⋊((C3⋊Dic3)⋊C3)C2semidirect
6. #64107⋊C3C2semidirect
7. #64106⋊C3C2semidirect
8. #64099⋊C3C2semidirect
9. #64098⋊C3C2semidirect
10. #64095⋊C3C2semidirect
11. #64092⋊C3C2semidirect
12. #64090⋊C3C2semidirect
13. #64088⋊C3C2semidirect
14. #64087⋊C3C2semidirect
15. #64087⋊C3C2semidirect
16. #10596136C3semidirect
54. C32×#123D3semidirect
55. C32×#123C2×C3semidirect
57. D4×C3⋊Dic3C2×C3semidirect
58. #64138C2×C3semidirect
59. C2×C4⋊(C3⋊Dic3)C2×C3semidirect
60. #64107C2×C3semidirect
61. #64106C2×C3semidirect
62. #64099C2×C3semidirect
63. #64098C2×C3semidirect
64. #64095C2×C3semidirect
65. #64092C2×C3semidirect
66. #64090C2×C3semidirect
67. #64088C2×C3semidirect
68. #64087C2×C3semidirect
69. #64087C2×C3semidirect
495. #123(C3⋊D3)⋊C3semidirect
503. H(3,𝔽3)#539semidirect
716. C32#5665semidirect
717. C32C3×#539semidirect

Maximal subgroups

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

subgroupindex
H(3,𝔽3)×#1232
#64148⋊C32
D4×(C3⋊Dic3)⋊C32
#64138⋊C32
C2×C4⋊((C3⋊Dic3)⋊C3)2
#64107⋊C32
#64106⋊C32
#64099⋊C32
#64098⋊C32
#64095⋊C32
#64092⋊C32
#64090⋊C32
#64088⋊C32
#64087⋊C32
#105961363
C3×#56653