Finite Group Databasebeta

← C3×#13180427 #72260115

Subgroups — C3×#13180427 #72260115

Order 5184.

1022 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#11724243C211yesmaximal, characteristic, complemented
2C3×#11724355C211yesmaximal, characteristic
3C2×C3×#89092C212yesmaximal, complemented
4C3×#11724102C212yesmaximal, complemented
5C22×C32×PSU(3,𝔽2)C211yesmaximal, characteristic, complemented
6#13180427C311yesmaximal, characteristic, direct product factor
7C3×#10596418—31nomaximal
8C22×C32×#157—21no—
9C22×C32×#157C2211yescharacteristic
10C2×C32×PSU(3,𝔽2)—21no—
11C2×C32×PSU(3,𝔽2)—24no—
12C2×C32×PSU(3,𝔽2)C2212yes—
13C2×C3×#157⋊D3C2211yescharacteristic
14C2×C3×C3⋊AGL(1,𝔽9)C2212yes—
15C3×#89092—24no—
16C3×#89049—21no—
17C3×#88940C2211yescharacteristic
18C3×#88939—21no—
19C22×C3×PSU(3,𝔽2)—21no—
20C22×C3×PSU(3,𝔽2)D311yescharacteristic, complemented
21C22×C3×PSU(3,𝔽2)C2×C311yescharacteristic, complemented
22C2×#89092C2×C312yescomplemented
23C2×C3×AΓL(1,𝔽9)—32no—
24#11724355C2×C311yescharacteristic
25C3×#64242—31no—
26#11724243C2×C311yescharacteristic, complemented
27C3×C22⋊AGL(1,𝔽9)—31no—
28#11724102C2×C312yescomplemented
29C3×PSU(3,𝔽2)⋊C4—32no—
30C22×C32×C3⋊D3D411yescharacteristic
31C2×C3×#1113—21no—
32C2×C32×#157—24no—
33C2×C32×#157—22no—
34C2×C32×#157—22no—
35C2×C32×#157D411yescharacteristic
36C2×C32×#157C2311yescharacteristic
37C32×PSU(3,𝔽2)—24no—
38C32×PSU(3,𝔽2)—22no—
39C32×PSU(3,𝔽2)D414yescomplemented
40C3×#157⋊D3—22no—
41C3×C3⋊AGL(1,𝔽9)—22no—
42C32×#638—41no—
43C3×#6295—41no—
44C3×#6294—21no—
45#10596418—31no—
46C3×#5227—91nomaximal
47C22×C3×#157—22no—
48C22×C3×#157—21no—
49C22×C3×#157—21no—
50C22×C3×#157—21no—
51C22×C3×#157C2×D311yescharacteristic
52C22×C3×#157C22×C311yescharacteristic
53C2×C3×PSU(3,𝔽2)—22no—
54C2×C3×PSU(3,𝔽2)—28no—
55C2×C3×PSU(3,𝔽2)—21no—
56C2×C3×PSU(3,𝔽2)—21no—
57C2×C3×PSU(3,𝔽2)—24no—
58C2×C3×PSU(3,𝔽2)—24no—
59C2×C3×PSU(3,𝔽2)—22no—
60C2×C3×PSU(3,𝔽2)C2×D312yes—
61C2×C3×PSU(3,𝔽2)C22×C312yes—
62C2×#157⋊D3C22×C311yescharacteristic
63C2×C3×GO+(4,𝔽2)—31no—
64C2×C3⋊AGL(1,𝔽9)C22×C312yes—
65C2×C3×AGL(1,𝔽9)—32no—
66#89092—24no—
67C3×AΓL(1,𝔽9)—64no—
68#89049—21no—
69C3×#3811—61no—
70C3×D3×#67—121no—
71#88940C22×C311yescharacteristic
72#88939—21no—
73C3×#3773—31no—
74C3×D32⋊C4—61no—
75C22×C34SD1611yescharacteristic, complemented
76C2×C32×C3⋊D3—21no—
77C2×C32×C3⋊D3—21no—
78C2×C32×C3⋊D3—41no—
79C2×C32×C3⋊D3SD1611yescharacteristic, complemented
80C2×C32×C3⋊D3C2×D411yescharacteristic
81C3×#1113—41no—
82C3×#1113—41no—
83C32×#157—21no—
84C32×#157—24no—
85C32×#157C2×D412yes—
86C32×C3⋊Dic3—41no—
87C22×PSU(3,𝔽2)C3×D311yescharacteristic, complemented
88C2×AΓL(1,𝔽9)—32no—
89C22×C32×Q8—91no—
90#64242—31no—
91C22⋊AGL(1,𝔽9)—31no—
92PSU(3,𝔽2)⋊C4—32no—
93C2×C3×#215—92no—
94C3×#930—91no—
95C3×#835—92no—
96C3×#830—91no—
97C22×C3×C3⋊D3—21no—
98C22×C3×C3⋊D3#6711yescharacteristic
99C22×C3×C3⋊D3C3×D411yescharacteristic
100C22×C32×D3—121no—
101C2×#1113—21no—
102C2×C3×D32—61no—
103C2×C3×D32—121no—
104C2×C3×#157—28no—
105C2×C3×#157—24no—
106C2×C3×#157—24no—
107C2×C3×#157—24no—
108C2×C3×#157—24no—
109C2×C3×#157—21no—
110C2×C3×#157—21no—
111C2×C3×#157—22no—
112C2×C3×#157—22no—
113C2×C3×#157—22no—
114C2×C3×#157—22no—
115C2×C3×#157#6711yescharacteristic
116C2×C3×#157C3×D411yescharacteristic
117C2×C3×#157C22×D311yescharacteristic
118C2×C3×#157C23×C311yescharacteristic
119C3×PSU(3,𝔽2)—28no—
120C3×PSU(3,𝔽2)—24no—
121C3×PSU(3,𝔽2)—24no—
122C3×PSU(3,𝔽2)—24no—
123C3×PSU(3,𝔽2)—24no—
124C3×PSU(3,𝔽2)—22no—
125C3×PSU(3,𝔽2)—22no—
126C3×PSU(3,𝔽2)#6714yescomplemented
127C3×PSU(3,𝔽2)C3×D414yescomplemented
128#157⋊D3—22no—
129C3×GO+(4,𝔽2)—62no—
130C3⋊AGL(1,𝔽9)—22no—
131C3×AGL(1,𝔽9)—62no—
132C3×#638—41no—
133C3×#638—41no—
134C3×#638—81no—
135C32×#67—121no—
136C32×#67—121no—
137C32×#67—241no—
138#6295—41no—
139#6294—21no—
140C3×#626—121no—
141C3×#626—121no—
142C3×#625—121no—
143C3×#624—61no—
144C3×D3×Dic3—121no—
145C3×#448—271no—
146#5227—91no—
147C2×C34—21no—
148C2×C34C2×SD1611yescharacteristic
149C32×C3⋊D3—21no—
150C32×C3⋊D3—81no—
151C32×C3⋊D3#12011yescharacteristic
152C32×C3⋊D3#13711yescharacteristic
153C22×#157—21no—
154C22×#157C2×C3×D311yescharacteristic
155C2×PSU(3,𝔽2)—21no—
156C2×PSU(3,𝔽2)—24no—
157C2×PSU(3,𝔽2)C2×C3×D312yes—
158C2×GO+(4,𝔽2)—31no—
159C2×AGL(1,𝔽9)—32no—
160AΓL(1,𝔽9)—64no—
161C2×C32×Q8—92no—
162C2×C32×Q8—181no—
163C2×C32×Q8—184no—
164C22×C32×C4—91no—
165C22×C32×C4—181no—
166C2×C3×#67—181no—
167C3×D3×D4—361no—
168C2×C3×D12—91no—
169#3811—61no—
170D3×#67—121no—
171#3773—31no—
172D32⋊C4—61no—
173C3×#215—184no—
174C3×(C2×D3)⋊C4—181no—
175C3×C4⋊Dic3—91no—
176C2×C3×C3⋊C8—92no—
177C22×C33—21no—
178C22×C33—41no—
179C22×C33—81no—
180C22×C33—81no—
181C22×C33—161no—
182C22×C33#21511yescharacteristic, complemented
183C22×C33C3×SD1611yescharacteristic, complemented
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—21no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—41no—
193C2×C3×C3⋊D3—41no—
194C2×C3×C3⋊D3—81no—
195C2×C3×C3⋊D3#21511yescharacteristic, complemented
196C2×C3×C3⋊D3C3×SD1611yescharacteristic, complemented
197C2×C3×C3⋊D3C2×#6711yescharacteristic
198C2×C3×C3⋊D3C2×C3×D411yescharacteristic
199C2×C32×D3—121no—
200C2×C32×D3—121no—
201C2×C32×D3—121no—
202C2×C32×D3—121no—
203C2×C32×D3—241no—
204C2×C32×D3—241no—
205C2×C32×D3—241no—
206#1113—41no—
207#1113—41no—
208C3×D32—121no—
209C3×D32—121no—
210C3×D32—241no—
211C3×D32—241no—
212C3×#157—22no—
213C3×#157—28no—
214C3×#157—22no—
215C3×#157—21no—
216C3×#157—24no—
217C3×#157—21no—
218C3×#157—24no—
219C3×#157C2×#6712yes—
220C3×#157C2×C3×D412yes—
221C3×C3⋊Dic3—41no—
222C3×C3⋊Dic3—41no—
223C3×C3⋊Dic3—81no—
224C32×Dic3—121no—
225C32×Dic3—121no—
226C32×Dic3—241no—
227C22×C3×Q8—91no—
228C22×C3×Q8—91no—
229C22×C3×Q8—181no—
230C2×C3×SD16—272no—
231C3×#121—271no—
232C2×#215—92no—
233#930—91no—
234C3×#103—272no—
235C3×C22⋊C8—271no—
236#835—92no—
237#830—91no—
238C34#44811yescharacteristic, complemented, Sylow
239C23×C32—91no—
240C22×C3⋊D3C3×#6711yescharacteristic
241C22×C3×D3—121no—
242C22×C3×D3—121no—
243C22×C3×D3—181no—
244C22×C3×D3—241no—
245C22×C3×D3—361no—
246C2×D32—61no—
247C2×D32—121no—
248C2×#157—24no—
249C2×#157—22no—
250C2×#157—22no—
251C2×#157C3×#6711yescharacteristic
252C2×#157C22×C3×D311yescharacteristic
253PSU(3,𝔽2)—24no—
254PSU(3,𝔽2)—22no—
255PSU(3,𝔽2)C3×#6714yescomplemented
256GO+(4,𝔽2)—62no—
257AGL(1,𝔽9)—62no—
258C32×Q8—94no—
259C32×Q8—182no—
260C32×Q8—184no—
261C32×D4—361no—
262C2×C32×C4—91no—
263C2×C32×C4—91no—
264C2×C32×C4—182no—
265C2×C32×C4—182no—
266C2×C32×C4—184no—
267#638—41no—
268C3×#67—121no—
269C3×#67—121no—
270C3×#67—121no—
271C3×#67—121no—
272C3×#67—241no—
273C3×#67—241no—
274C3×#67—241no—
275C3×#67—241no—
276C3×#67—242no—
277C3×#67—361no—
278C3×#67—361no—
279C2×C3×Dic3—181no—
280C3×D12—182no—
281C3×D12—361no—
282C3×C4×D3—361no—
283#626—121no—
284#626—121no—
285#625—121no—
286#624—61no—
287D3×Dic3—121no—
288C3×C3⋊C8—182no—
289#448—271noSylow
290C2×C33—22no—
291C2×C33—21no—
292C2×C33—21no—
293C2×C33—21no—
294C2×C33—41no—
295C2×C33—81no—
296C2×C33—81no—
297C2×C33—81no—
298C2×C33—161no—
299C2×C33—161no—
300C2×C33—161no—
301C2×C33—162no—
302C2×C33C2×#21511yescharacteristic
303C2×C33C2×C3×SD1611yescharacteristic
304C3×C3⋊D3—22no—
305C3×C3⋊D3—21no—
306C3×C3⋊D3—21no—
307C3×C3⋊D3—21no—
308C3×C3⋊D3—21no—
309C3×C3⋊D3—81no—
310C3×C3⋊D3—81no—
311C3×C3⋊D3—161no—
312C3×C3⋊D3#94211yescharacteristic
313C3×C3⋊D3#95311yescharacteristic
314C3×C3⋊D3C3×#12011yescharacteristic
315C3×C3⋊D3C3×#13711yescharacteristic
316C32×D3—121no—
317C32×D3—121no—
318C32×D3—241no—
319C32×D3—241no—
320C32×D3—241no—
321C32×D3—481no—
322C2×C3×Q8—92no—
323C2×C3×Q8—92no—
324C2×C3×Q8—182no—
325C2×C3×Q8—181no—
326C2×C3×Q8—181no—
327C2×C3×Q8—184no—
328C2×C3×Q8—184no—
329C2×C3×Q8—182no—
330C2×C3×Q8—188no—
331C2×C3×D4—271no—
332C2×C3×D4—541no—
333C22×C3×C4—91no—
334C22×C3×C4—91no—
335C22×C3×C4—181no—
336C22×C3×C4—181no—
337C22×C3×C4—181no—
338C22×C3×C4—182no—
339C2×#67—181no—
340D3×D4—361no—
341C2×D12—91no—
342C3×SD16—544no—
343C2×C3×C8—272no—
344C3×C4⋊C4—271no—
345C3×C22⋊C4—541no—
346#215—184no—
347(C2×D3)⋊C4—181no—
348C4⋊Dic3—91no—
349C2×C3⋊C8—92no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—81no—
353C22×C32—81no—
354C22×C32—81no—
355C22×C32—82no—
356C22×C32—81no—
357C22×C32—81no—
358C22×C32—91no—
359C22×C32—91no—
360C22×C32—161no—
361C22×C32—161no—
362C22×C32—162no—
363C22×C32—181no—
364C22×C32—181no—
365C22×C32—361no—
366C22×C32C3×#21511yescharacteristic, complemented
367C22×C32AΓL(1,𝔽9)11yescharacteristic, complemented
368C2×C3⋊D3—21no—
369C2×C3⋊D3—21no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3C3×#21511yescharacteristic, complemented
372C2×C3⋊D3C2×C3×#6711yescharacteristic
373C2×C3×D3—121no—
374C2×C3×D3—121no—
375C2×C3×D3—121no—
376C2×C3×D3—121no—
377C2×C3×D3—121no—
378C2×C3×D3—121no—
379C2×C3×D3—121no—
380C2×C3×D3—121no—
381C2×C3×D3—241no—
382C2×C3×D3—241no—
383C2×C3×D3—241no—
384C2×C3×D3—241no—
385C2×C3×D3—241no—
386C2×C3×D3—241no—
387C2×C3×D3—241no—
388C2×C3×D3—241no—
389C2×C3×D3—242no—
390C2×C3×D3—242no—
391C2×C3×D3—241no—
392C2×C3×D3—241no—
393C2×C3×D3—242no—
394C2×C3×D3—361no—
395C2×C3×D3—361no—
396C2×C3×D3—721no—
397C2×C3×D3—721no—
398D32—121no—
399D32—121no—
400D32—241no—
401D32—241no—
402#157—21no—
403#157—24no—
404#157C2×C3×#6712yes—
405C32×C4—92no—
406C32×C4—181no—
407C32×C4—184no—
408C32×C4—361no—
409C3⋊Dic3—41no—
410C3×Dic3—121no—
411C3×Dic3—121no—
412C3×Dic3—121no—
413C3×Dic3—121no—
414C3×Dic3—241no—
415C3×Dic3—241no—
416C3×Dic3—241no—
417C3×Dic3—241no—
418C3×Dic3—242no—
419C22×Q8—91no—
420C2×SD16—272no—
421#121—271no—
422#103—272no—
423C22⋊C8—271no—
424C33—21no—
425C33—41no—
426C33—81no—
427C33—81no—
428C33—161no—
429C33#522711yescharacteristic, complemented
430C33C3×#44811yescharacteristic, complemented
431C23×C3—91no—
432C23×C3—91no—
433C23×C3—181no—
434C23×C3—541no—
435C22×D3—121no—
436C22×D3—181no—
437C22×D3—361no—
438C3×Q8—94no—
439C3×Q8—94no—
440C3×Q8—184no—
441C3×Q8—182no—
442C3×Q8—182no—
443C3×Q8—184no—
444C3×Q8—184no—
445C3×Q8—184no—
446C3×Q8—188no—
447C3×D4—361no—
448C3×D4—361no—
449C3×D4—542no—
450C3×D4—721no—
451C3×D4—1081no—
452C2×C3×C4—91no—
453C2×C3×C4—91no—
454C2×C3×C4—91no—
455C2×C3×C4—91no—
456C2×C3×C4—181no—
457C2×C3×C4—181no—
458C2×C3×C4—182no—
459C2×C3×C4—182no—
460C2×C3×C4—182no—
461C2×C3×C4—182no—
462C2×C3×C4—184no—
463C2×C3×C4—184no—
464C2×C3×C4—184no—
465C2×C3×C4—184no—
466C2×C3×C4—188no—
467C2×C3×C4—541no—
468#67—121no—
469#67—121no—
470#67—241no—
471#67—361no—
472#67—361no—
473C2×Dic3—181no—
474D12—182no—
475D12—361no—
476C4×D3—361no—
477C3×C8—542no—
478C3⋊C8—182no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—41no—
482C2×C32—41no—
483C2×C32—81no—
484C2×C32—81no—
485C2×C32—81no—
486C2×C32—82no—
487C2×C32—81no—
488C2×C32—81no—
489C2×C32—82no—
490C2×C32—81no—
491C2×C32—81no—
492C2×C32—91no—
493C2×C32—91no—
494C2×C32—161no—
495C2×C32—161no—
496C2×C32—161no—
497C2×C32—162no—
498C2×C32—161no—
499C2×C32—162no—
500C2×C32—161no—
501C2×C32—161no—
502C2×C32—162no—
503C2×C32—162no—
504C2×C32—164no—
505C2×C32—181no—
506C2×C32—721no—
507C2×C32C2×C3×#21511yescharacteristic
508C2×C32C2×AΓL(1,𝔽9)11yescharacteristic
509C3⋊D3—21no—
510C3⋊D3—81no—
511C3⋊D3C3×#94211yescharacteristic
512C3⋊D3C3×#95311yescharacteristic
513C3×D3—121no—
514C3×D3—121no—
515C3×D3—121no—
516C3×D3—121no—
517C3×D3—241no—
518C3×D3—241no—
519C3×D3—241no—
520C3×D3—241no—
521C3×D3—242no—
522C3×D3—241no—
523C3×D3—241no—
524C3×D3—241no—
525C3×D3—241no—
526C3×D3—481no—
527C3×D3—481no—
528C3×D3—481no—
529C3×D3—481no—
530C3×D3—482no—
531C2×Q8—92no—
532C2×Q8—181no—
533C2×Q8—184no—
534C2×D4—271no—
535C2×D4—541no—
536C22×C4—91no—
537C22×C4—181no—
538SD16—544no—
539C2×C8—272no—
540C4⋊C4—271no—
541C22⋊C4—541no—
542C22×C3—21no—
543C22×C3—41no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—91no—
547C22×C3—91no—
548C22×C3—91no—
549C22×C3—91no—
550C22×C3—161no—
551C22×C3—181no—
552C22×C3—181no—
553C22×C3—181no—
554C22×C3—181no—
555C22×C3—181no—
556C22×C3—181no—
557C22×C3—182no—
558C22×C3—182no—
559C22×C3—361no—
560C22×C3—361no—
561C22×C3—721no—
562C22×C3—1081no—
563C22×C3—1081no—
564C22×C3C3×AΓL(1,𝔽9)11yescharacteristic, complemented
565C22×C3#8909211yescharacteristic, complemented
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—241no—
571C2×D3—241no—
572C2×D3—241no—
573C2×D3—361no—
574C2×D3—361no—
575C2×D3—721no—
576C2×D3—721no—
577C3×C4—92no—
578C3×C4—92no—
579C3×C4—182no—
580C3×C4—181no—
581C3×C4—181no—
582C3×C4—184no—
583C3×C4—184no—
584C3×C4—182no—
585C3×C4—188no—
586C3×C4—361no—
587C3×C4—361no—
588C3×C4—721no—
589Dic3—121no—
590Dic3—121no—
591Dic3—241no—
592C32—41no—
593C32—41no—
594C32—81no—
595C32—81no—
596C32—81no—
597C32—82no—
598C32—81no—
599C32—81no—
600C32—161no—
601C32—161no—
602C32—162no—
603C32C3×#522711yescharacteristic, complemented
604C32#1059641811yescharacteristic, complemented
605C23—91no—
606C23—541no—
607Q8—94no—
608Q8—182no—
609Q8—184no—
610D4—361no—
611D4—542no—
612D4—1081no—
613C2×C4—91no—
614C2×C4—91no—
615C2×C4—182no—
616C2×C4—182no—
617C2×C4—184no—
618C2×C4—541no—
619C8—542no—
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—41no—
625C2×C3—81no—
626C2×C3—81no—
627C2×C3—81no—
628C2×C3—91no—
629C2×C3—91no—
630C2×C3—91no—
631C2×C3—91no—
632C2×C3—161no—
633C2×C3—161no—
634C2×C3—162no—
635C2×C3—161no—
636C2×C3—181no—
637C2×C3—181no—
638C2×C3—182no—
639C2×C3—181no—
640C2×C3—181no—
641C2×C3—721no—
642C2×C3—721no—
643C2×C3—1441no—
644C2×C3C2×C3×AΓL(1,𝔽9)11yescharacteristic
645C2×C3C2×#8909211yescharacteristic
646D3—121no—
647D3—121no—
648D3—241no—
649D3—241no—
650D3—241no—
651D3—481no—
652C22—91no—
653C22—91no—
654C22—181no—
655C22—181no—
656C22—361no—
657C22—1081no—
658C22—1081no—
659C22C3×#8909211yescharacteristic, complemented
660C4—92no—
661C4—181no—
662C4—184no—
663C4—361no—
664C3—21no—
665C3—41no—
666C3—81no—
667C3—81no—
668C3—161no—
669C3C3×#1059641811yescharacteristic, complemented
670C3#1318042711yescharacteristic, direct product factor
671C2—21no—
672C2—91no—
673C2—91no—
674C2—181no—
675C2—721no—
676C2C2×C3×#8909211yescharacteristic
subgroupG/H
centerC2×C3C2×#89092
commutator, cosocleC2×C3×#157C23×C3
FrattiniC2C2×C3×#89092
FittingC22×C34SD16
socleC2×C34C2×SD16
prime radicalC3×#11724355C2
hypercenterC22×C3#89092
hypocenterC33C3×#448
LCSG ▷ C2×C3×#157 ▷ C3×C3⋊D3 ▷ C33
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C3×#11724243C2semidirect
3. C2×C3×#89092C2semidirect
4. C3×#11724102C2semidirect
5. C22×C32×PSU(3,𝔽2)C2semidirect
6. #13180427C3direct (N × H)
20. C22×C3×PSU(3,𝔽2)D3semidirect
21. C22×C3×PSU(3,𝔽2)C2×C3semidirect
22. C2×#89092C2×C3semidirect
26. #11724243C2×C3semidirect
28. #11724102C2×C3semidirect
39. C32×PSU(3,𝔽2)D4semidirect
75. C22×C34SD16semidirect
79. C2×C32×C3⋊D3SD16semidirect
87. C22×PSU(3,𝔽2)C3×D3semidirect
126. C3×PSU(3,𝔽2)#67semidirect
127. C3×PSU(3,𝔽2)C3×D4semidirect
182. C22×C33#215semidirect
183. C22×C33C3×SD16semidirect
195. C2×C3×C3⋊D3#215semidirect
196. C2×C3×C3⋊D3C3×SD16semidirect
238. C34#448semidirect
255. PSU(3,𝔽2)C3×#67semidirect
366. C22×C32C3×#215semidirect
367. C22×C32AΓL(1,𝔽9)semidirect
371. C2×C3⋊D3C3×#215semidirect
429. C33#5227semidirect
430. C33C3×#448semidirect
564. C22×C3C3×AΓL(1,𝔽9)semidirect
565. C22×C3#89092semidirect
603. C32C3×#5227semidirect
604. C32#10596418semidirect
659. C22C3×#89092semidirect
669. C3C3×#10596418semidirect
670. C3#13180427direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#117242432
C3×#117243552
C2×C3×#890922
C3×#117241022
C22×C32×PSU(3,𝔽2)2
#131804273
C3×#105964183
C3×#52279