Finite Group Databasebeta

← #10592655⋊C3 #13142506

Subgroups — #10592655⋊C3 #13142506

Order 1728.

1133 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#638⋊C3C211yesmaximal, characteristic
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
4C2×#3757⋊C3C211yesmaximal, characteristic, complemented
5C2×#3752⋊C3C211yesmaximal, characteristic, complemented
6#63658⋊C3C211yesmaximal, characteristic, complemented
7#63658⋊C3C211yesmaximal, characteristic, complemented
8#10592655C311yesmaximal, characteristic, complemented
9C3×#4956—31nomaximal
10C24×H(3,𝔽3)C2211yescharacteristic
11C23×(C3⋊D3)⋊C3C2211yescharacteristic
12C22×C4×H(3,𝔽3)C2211yescharacteristic
13C22×C4×H(3,𝔽3)C2211yescharacteristic
14C2×#638⋊C3—22no—
15C2×#638⋊C3—22no—
16C2×#638⋊C3C414yescomplemented
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3—22no—
21C2×C4×(C3⋊D3)⋊C3—22no—
22C2×C4×(C3⋊D3)⋊C3—22no—
23C22⋊C4×H(3,𝔽3)—22no—
24#3757⋊C3—22no—
25#3752⋊C3—22no—
26C22×#638C2×C311yescharacteristic
27C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
28C22×C3×#67—31no—
29C22×C3×C4×D3—31no—
30C2×C32×C22⋊C4—21no—
31C2×C32×C22⋊C4D311yescharacteristic, complemented
32C2×C32×C22⋊C4C2×C311yescharacteristic, complemented
33C2×#3757C2×C311yescharacteristic, complemented
34C2×#3752C2×C311yescharacteristic, complemented
35C2×C3×#217—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37#63658C2×C311yescharacteristic, complemented
38#63658C2×C311yescharacteristic, complemented
39C3×C3⋊#95—31no—
40C3×C3⋊#95—31no—
41C23×H(3,𝔽3)—21no—
42C23×H(3,𝔽3)—21no—
43C23×H(3,𝔽3)—21no—
44C23×H(3,𝔽3)—21no—
45C23×H(3,𝔽3)—21no—
46C23×H(3,𝔽3)—21no—
47C23×H(3,𝔽3)C2×C412yescomplemented
48C23×H(3,𝔽3)C2311yescharacteristic
49C22×(C3⋊D3)⋊C3—21no—
50C22×(C3⋊D3)⋊C3—21no—
51C22×(C3⋊D3)⋊C3—21no—
52C22×(C3⋊D3)⋊C3—21no—
53C22×(C3⋊D3)⋊C3C2×C412yes—
54C22×(C3⋊D3)⋊C3D412yes—
55C22×(C3⋊D3)⋊C3D412yes—
56C2×C4×H(3,𝔽3)—21no—
57C2×C4×H(3,𝔽3)—21no—
58C2×C4×H(3,𝔽3)—21no—
59C2×C4×H(3,𝔽3)—21no—
60C2×C4×H(3,𝔽3)—21no—
61C2×C4×H(3,𝔽3)D412yescomplemented
62#638⋊C3—28no—
63C2×(C3⋊Dic3)⋊C3—21no—
64C2×(C3⋊Dic3)⋊C3—21no—
65C2×(C3⋊Dic3)⋊C3—21no—
66C2×(C3⋊Dic3)⋊C3—21no—
67C2×(C3⋊Dic3)⋊C3—21no—
68C2×(C3⋊Dic3)⋊C3—21no—
69C2×(C3⋊Dic3)⋊C3—21no—
70C2×(C3⋊Dic3)⋊C3C2×C412yescomplemented
71C2×(C3⋊Dic3)⋊C3D412yescomplemented
72C4×(C3⋊D3)⋊C3—28no—
73C3×#386—91no—
74#4956—31no—
75#4956—91no—
76C24×C32—21no—
77C24×C32C2×D311yescharacteristic
78C24×C32C22×C311yescharacteristic
79C23×C3⋊D3C22×C311yescharacteristic
80C23×C3×D3—31no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C22×C311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C2×#638—22no—
88C2×#638—22no—
89C2×#638C3×C414yescomplemented
90C22×C3⋊Dic3C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3⋊Dic3C22×C311yescharacteristic
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×C3×#67—34no—
97C2×C3×#67—62no—
98C2×C3×#67—62no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C2×C3×C4×D3—62no—
103C2×C3×C4×D3—62no—
104C2×C3×C4×D3—62no—
105C32×C22⋊C4—24no—
106C32×C22⋊C4—22no—
107C32×C22⋊C4—22no—
108#3757—22no—
109#3752—22no—
110C3×#217—62no—
111C3×(C2×D3)⋊C4—62no—
112C22×H(3,𝔽3)—22no—
113C22×H(3,𝔽3)—22no—
114C22×H(3,𝔽3)—22no—
115C22×H(3,𝔽3)—41no—
116C22×H(3,𝔽3)—41no—
117C22×H(3,𝔽3)—41no—
118C22×H(3,𝔽3)—41no—
119C22×H(3,𝔽3)C22×C411yescharacteristic
120C22×H(3,𝔽3)C2×D411yescharacteristic
121C22×H(3,𝔽3)C2×D411yescharacteristic
122C22×H(3,𝔽3)C2×D411yescharacteristic
123C22×H(3,𝔽3)C2×D411yescharacteristic
124C22×H(3,𝔽3)#4111yescharacteristic
125C22×H(3,𝔽3)#4111yescharacteristic
126C2×(C3⋊D3)⋊C3—22no—
127C2×(C3⋊D3)⋊C3—22no—
128C2×(C3⋊D3)⋊C3—22no—
129C2×(C3⋊D3)⋊C3—22no—
130C2×(C3⋊D3)⋊C3—22no—
131C2×(C3⋊D3)⋊C3—22no—
132C2×(C3⋊D3)⋊C3C22⋊C414yescomplemented
133C4×H(3,𝔽3)—22no—
134C4×H(3,𝔽3)—41no—
135(C3⋊Dic3)⋊C3—22no—
136(C3⋊Dic3)⋊C3—22no—
137(C3⋊Dic3)⋊C3—41no—
138C22×C3×D4—91no—
139C23×C3×C4—91no—
140C22×#67—31no—
141C22×#67—91no—
142C22×C4×D3—31no—
143C22×C4×D3—91no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—61no—
147C2×C3×C22⋊C4—91no—
148C2×C3×C22⋊C4—91no—
149C2×C3×C22⋊C4C3×D311yescharacteristic
150C2×#217—31no—
151C2×#217—91no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—91no—
154C3×#95—91no—
155C3×#95—91no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—91no—
159C3⋊#95—91no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—21no—
176C23×C32—41no—
177C23×C32—41no—
178C23×C32—41no—
179C23×C32—41no—
180C23×C32C4×D312yescomplemented
181C23×C32C2×C3×C412yescomplemented
182C23×C32C22×D311yescharacteristic
183C23×C32C23×C311yescharacteristic
184C22×C3⋊D3—21no—
185C22×C3⋊D3—21no—
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3C2×C3×C412yes—
189C22×C3⋊D3C3×D412yes—
190C22×C3⋊D3C3×D412yes—
191C22×C3×D3—32no—
192C22×C3×D3—32no—
193C22×C3×D3—32no—
194C22×C3×D3—61no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3—61no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—22no—
210C2×C32×C4—41no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4#6712yescomplemented
215C2×C32×C4C3×D412yescomplemented
216#638—28no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3C2×C3×C412yescomplemented
225C2×C3⋊Dic3C3×D412yescomplemented
226C4×C3⋊D3—28no—
227C3×#67—68no—
228C2×C3×Dic3—32no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—61no—
233C2×C3×Dic3—61no—
234C2×C3×Dic3—61no—
235C2×C3×Dic3—61no—
236C2×C3×Dic3—61no—
237C3×C4×D3—68no—
238#386—91noSylow
239C2×H(3,𝔽3)—42no—
240C2×H(3,𝔽3)C2×C22⋊C411yescharacteristic
241C2×H(3,𝔽3)C4×D411yescharacteristic
242C2×H(3,𝔽3)C4×D411yescharacteristic
243C2×H(3,𝔽3)#12011yescharacteristic
244C2×H(3,𝔽3)#12111yescharacteristic
245C2×H(3,𝔽3)#12111yescharacteristic
246C2×H(3,𝔽3)#12311yescharacteristic
247(C3⋊D3)⋊C3—24no—
248C24×C3—31no—
249C24×C3—31no—
250C24×C3—61no—
251C24×C3—91no—
252C24×C3C2×C3×D311yescharacteristic
253C23×D3—31no—
254C23×D3—91no—
255C2×C3×D4—94no—
256C2×C3×D4—182no—
257C2×C3×D4—182no—
258C22×C3×C4—31no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—91no—
265C22×C3×C4—91no—
266C22×C3×C4—91no—
267C22×C3×C4—182no—
268C22×C3×C4—182no—
269C22×C3×C4—182no—
270C22×C3×C4C2×C3×D311yescharacteristic
271C22×C3×C4C2×C3×D311yescharacteristic
272C2×#67—34no—
273C2×#67—62no—
274C2×#67—62no—
275C2×#67—94no—
276C2×#67—182no—
277C2×#67—182no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—31no—
281C22×Dic3—91no—
282C22×Dic3—91no—
283C22×Dic3—91no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—182no—
288C2×C4×D3—182no—
289C2×C4×D3—182no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—62no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—182no—
295C3×C22⋊C4—182no—
296#217—62no—
297#217—182no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—182no—
300C22×C32—24no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—42no—
315C22×C32—42no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32—42no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
327C22×C32—41no—
328C22×C32C2×C4×D311yescharacteristic
329C22×C32#23511yescharacteristic
330C22×C32D3×D411yescharacteristic
331C22×C32D3×D411yescharacteristic
332C22×C32D3×D411yescharacteristic
333C22×C32#23711yescharacteristic
334C22×C32C2×#6711yescharacteristic
335C22×C32C22×C3×C411yescharacteristic
336C22×C32C2×C3×D411yescharacteristic
337C22×C32C2×C3×D411yescharacteristic
338C22×C32C2×C3×D411yescharacteristic
339C22×C32C2×C3×D411yescharacteristic
340C22×C32C3×#4111yescharacteristic
341C22×C32C3×#4111yescharacteristic
342C2×C3⋊D3—22no—
343C2×C3⋊D3—22no—
344C2×C3⋊D3—22no—
345C2×C3⋊D3—22no—
346C2×C3⋊D3—22no—
347C2×C3⋊D3—22no—
348C2×C3⋊D3C3×C22⋊C414yescomplemented
349C2×C3×D3—34no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—62no—
355C2×C3×D3—62no—
356C32×C4—22no—
357C32×C4—22no—
358C32×C4—42no—
359C32×C4—42no—
360C32×C4—41no—
361C32×C4—41no—
362C3⋊Dic3—22no—
363C3⋊Dic3—22no—
364C3⋊Dic3—41no—
365C3×Dic3—62no—
366C3×Dic3—62no—
367C3×Dic3—121no—
368C22×D4—91no—
369C23×C4—91no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—91no—
372C2×C22⋊C4(C3⋊D3)⋊C311yescharacteristic, complemented
373#95—91no—
374#95—91no—
375H(3,𝔽3)#38611yescharacteristic, complemented, Sylow
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—32no—
383C23×C3—32no—
384C23×C3—31no—
385C23×C3—31no—
386C23×C3—61no—
387C23×C3—61no—
388C23×C3—61no—
389C23×C3—61no—
390C23×C3—61no—
391C23×C3—61no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—62no—
399C23×C3—62no—
400C23×C3—62no—
401C23×C3—61no—
402C23×C3—92no—
403C23×C3—92no—
404C23×C3—92no—
405C23×C3—121no—
406C23×C3—121no—
407C23×C3—121no—
408C23×C3—121no—
409C23×C3—181no—
410C23×C3—181no—
411C23×C3—181no—
412C23×C3—181no—
413C23×C3C3×C4×D312yes—
414C23×C3C22×C3×D311yescharacteristic
415C22×D3—32no—
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—92no—
423C22×D3—92no—
424C22×D3—92no—
425C22×D3—181no—
426C22×D3—181no—
427C22×D3—181no—
428C22×D3—181no—
429C3×D4—188no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—32no—
436C2×C3×C4—32no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—92no—
450C2×C3×C4—92no—
451C2×C3×C4—121no—
452C2×C3×C4—121no—
453C2×C3×C4—121no—
454C2×C3×C4—121no—
455C2×C3×C4—188no—
456C2×C3×C4—181no—
457C2×C3×C4—181no—
458C2×C3×C4—181no—
459C2×C3×C4—181no—
460C2×C3×C4—181no—
461C2×C3×C4—181no—
462C2×C3×C4—181no—
463C2×C3×C4C3×#6712yes—
464#67—68no—
465#67—188no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—92no—
476C2×Dic3—92no—
477C2×Dic3—181no—
478C2×Dic3—181no—
479C2×Dic3—181no—
480C2×Dic3—181no—
481C2×Dic3—181no—
482C2×Dic3—181no—
483C2×Dic3—181no—
484C4×D3—68no—
485C4×D3—188no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—44no—
494C2×C32—42no—
495C2×C32—42no—
496C2×C32D3×C22⋊C411yescharacteristic
497C2×C32#67⋊C411yescharacteristic
498C2×C32#88311yescharacteristic
499C2×C32#88411yescharacteristic
500C2×C32C4×#6711yescharacteristic
501C2×C32#93711yescharacteristic
502C2×C32#93811yescharacteristic
503C2×C32C2×C3×C22⋊C411yescharacteristic
504C2×C32C3×C4×D411yescharacteristic
505C2×C32C3×C4×D411yescharacteristic
506C2×C32C3×#12011yescharacteristic
507C2×C32C3×#12111yescharacteristic
508C2×C32C3×#12111yescharacteristic
509C2×C32C3×#12311yescharacteristic
510C3⋊D3—24no—
511C3×D3—64no—
512C24—91no—
513C24C2×(C3⋊D3)⋊C311yescharacteristic
514C2×D4—94no—
515C2×D4—182no—
516C2×D4—182no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—182no—
521C22×C4—182no—
522C22×C4—182no—
523C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
524C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
525C22⋊C4—22no—
526C22⋊C4—182no—
527C22⋊C4—182no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—31no—
532C22×C3—31no—
533C22×C3—31no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—31no—
537C22×C3—31no—
538C22×C3—31no—
539C22×C3—31no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—31no—
543C22×C3—31no—
544C22×C3—31no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—64no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—61no—
559C22×C3—61no—
560C22×C3—61no—
561C22×C3—61no—
562C22×C3—61no—
563C22×C3—94no—
564C22×C3—122no—
565C22×C3—122no—
566C22×C3—121no—
567C22×C3—121no—
568C22×C3—121no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3—121no—
574C22×C3—122no—
575C22×C3—122no—
576C22×C3—122no—
577C22×C3—122no—
578C22×C3—182no—
579C22×C3—182no—
580C22×C3—182no—
581C22×C3—182no—
582C22×C3—182no—
583C22×C3—182no—
584C22×C3C2×C3×C4×D311yescharacteristic
585C22×C3C3×#23511yescharacteristic
586C22×C3C3×D3×D411yescharacteristic
587C22×C3C3×D3×D411yescharacteristic
588C22×C3C3×D3×D411yescharacteristic
589C22×C3C3×#23711yescharacteristic
590C22×C3C2×C3×#6711yescharacteristic
591C2×D3—34no—
592C2×D3—62no—
593C2×D3—62no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—94no—
599C2×D3—182no—
600C2×D3—182no—
601C2×D3—182no—
602C2×D3—182no—
603C2×D3—182no—
604C2×D3—182no—
605C3×C4—22no—
606C3×C4—41no—
607C3×C4—62no—
608C3×C4—62no—
609C3×C4—122no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4—122no—
613C3×C4—182no—
614C3×C4—182no—
615C3×C4—361no—
616Dic3—62no—
617Dic3—62no—
618Dic3—121no—
619Dic3—182no—
620Dic3—182no—
621Dic3—361no—
622C32—21no—
623C32#495611yescharacteristic, complemented
624C32C3×#38611yescharacteristic, complemented
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—92no—
632C23—92no—
633C23—92no—
634C23—181no—
635C23—181no—
636C23—181no—
637C23—181no—
638C23C4×(C3⋊D3)⋊C312yescomplemented
639C23C22×(C3⋊D3)⋊C311yescharacteristic
640D4—188no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—92no—
647C2×C4—92no—
648C2×C4—188no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4#638⋊C312yescomplemented
657C2×C3—31no—
658C2×C3—31no—
659C2×C3—31no—
660C2×C3—31no—
661C2×C3—31no—
662C2×C3—31no—
663C2×C3—31no—
664C2×C3—31no—
665C2×C3—31no—
666C2×C3—31no—
667C2×C3—31no—
668C2×C3—31no—
669C2×C3—31no—
670C2×C3—31no—
671C2×C3—42no—
672C2×C3—61no—
673C2×C3—61no—
674C2×C3—61no—
675C2×C3—61no—
676C2×C3—61no—
677C2×C3—61no—
678C2×C3—61no—
679C2×C3—122no—
680C2×C3—122no—
681C2×C3—124no—
682C2×C3—184no—
683C2×C3C3×D3×C22⋊C411yescharacteristic
684C2×C3C3×#67⋊C411yescharacteristic
685C2×C3C3×#88311yescharacteristic
686C2×C3C3×#88411yescharacteristic
687C2×C3C3×C4×#6711yescharacteristic
688C2×C3C3×#93711yescharacteristic
689C2×C3C3×#93811yescharacteristic
690D3—64no—
691D3—184no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—94no—
700C22—182no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22C2×C4×(C3⋊D3)⋊C311yescharacteristic
707C22#3828⋊C311yescharacteristic
708C22D4×(C3⋊D3)⋊C311yescharacteristic
709C22D4×(C3⋊D3)⋊C311yescharacteristic
710C22D4×(C3⋊D3)⋊C311yescharacteristic
711C22#3830⋊C311yescharacteristic
712C22C2×#638⋊C311yescharacteristic
713C4—22no—
714C4—41no—
715C4—182no—
716C4—182no—
717C4—361no—
718C3—31no—
719C3—31no—
720C3—61no—
721C3C3×#495611yescharacteristic
722C2—42no—
723C2—184no—
724C2C22⋊C4×(C3⋊D3)⋊C311yescharacteristic
725C2#64090⋊C311yescharacteristic
726C2#64092⋊C311yescharacteristic
727C2#64093⋊C311yescharacteristic
728C2C4×#638⋊C311yescharacteristic
729C2#64146⋊C311yescharacteristic
730C2#64147⋊C311yescharacteristic
subgroupG/H
centerC23C22×(C3⋊D3)⋊C3
commutatorC22×C32C22×C3×C4
Frattini, socleC23×C3C22×C3×D3
FittingC2×C22⋊C4×H(3,𝔽3)C2
prime radicalC22×#638⋊C3C2
cosocleC23×C32C23×C3
hypercenterC2×C22⋊C4(C3⋊D3)⋊C3
hypocenterC32C3×#386
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. C2×C22⋊C4×H(3,𝔽3)C2semidirect
4. C2×#3757⋊C3C2semidirect
5. C2×#3752⋊C3C2semidirect
6. #63658⋊C3C2semidirect
7. #63658⋊C3C2semidirect
8. #10592655C3semidirect
16. C2×#638⋊C3C4semidirect
27. C22×C4×C3⋊D3C2×C3semidirect
31. C2×C32×C22⋊C4D3semidirect
32. C2×C32×C22⋊C4C2×C3semidirect
33. C2×#3757C2×C3semidirect
34. C2×#3752C2×C3semidirect
37. #63658C2×C3semidirect
38. #63658C2×C3semidirect
47. C23×H(3,𝔽3)C2×C4semidirect
61. C2×C4×H(3,𝔽3)D4semidirect
70. C2×(C3⋊Dic3)⋊C3C2×C4semidirect
71. C2×(C3⋊Dic3)⋊C3D4semidirect
89. C2×#638C3×C4semidirect
132. C2×(C3⋊D3)⋊C3C22⋊C4semidirect
180. C23×C32C4×D3semidirect
181. C23×C32C2×C3×C4semidirect
214. C2×C32×C4#67semidirect
215. C2×C32×C4C3×D4semidirect
224. C2×C3⋊Dic3C2×C3×C4semidirect
225. C2×C3⋊Dic3C3×D4semidirect
348. C2×C3⋊D3C3×C22⋊C4semidirect
372. C2×C22⋊C4(C3⋊D3)⋊C3semidirect
375. H(3,𝔽3)#386semidirect
623. C32#4956semidirect
624. C32C3×#386semidirect
638. C23C4×(C3⋊D3)⋊C3semidirect
656. C2×C4#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×#638⋊C32
C22×C4×(C3⋊D3)⋊C32
C2×C22⋊C4×H(3,𝔽3)2
C2×#3757⋊C32
C2×#3752⋊C32
#63658⋊C32
#105926553
C3×#49563