Finite Group Databasebeta

← C2×#72221862 #72244166

Subgroups — C2×#72221862 #72244166

Order 17496.

1274 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 1274 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#72221859—31nomaximal
2C2×#72221850C311yesmaximal, characteristic
3C2×#72221838C211yesmaximal, characteristic, complemented
4C2×#10624472⋊C2—21no—
5C2×#92172⋊C3C2×C311yescharacteristic
6C2×#72221832C211yesmaximal, characteristic, complemented
7C2×C3⋊D3×C9⋊C9D311yescharacteristic
8C2×#13090876—21no—
9C2×#13090876C2×C311yescharacteristic
10C2×#72221821C211yesmaximal, characteristic, complemented
11C2×C3×C3⋊(D9⋊C9)—31no—
12C2×C3×C3⋊(D9⋊C9)—31no—
13C2×#13090878C2×C311yescharacteristic
14C2×#14550484C2211yescharacteristic, complemented
15C2×D3×AGL(1,ℤ/27)—31nomaximal
16C2×C3⋊AGL(1,ℤ/27)D311yescharacteristic, complemented
17C2×D3×#6875—31no—
18#72221862C214yesmaximal, direct product factor
19#72221859—34no—
20#72221850C2×C314yes—
21#72221838C2212yescomplemented
22#72221832C2212yescomplemented
23#72221821C2212yescomplemented
24D3×AGL(1,ℤ/27)—34no—
25C2×C3×AGL(1,ℤ/27)—31no—
26C2×C3×AGL(1,ℤ/27)—61no—
27#14550484C2311yescharacteristic, complemented, Sylow
28C2×C9×#1113—91no—
29C2×C3×#66431—31no—
30C2×D3×D27⋊C3—31no—
31C2×D3×D9⋊C9—91no—
32C2×D3×D9⋊C9—91no—
33C22×AGL(1,ℤ/27)—91no—
34C2×((C3⋊D3)⋊C27)⋊C2C911yescharacteristic, complemented
35C3×C3⋊(D9⋊C9)—32no—
36C3×C3⋊(D9⋊C9)—32no—
37C3⋊D3×C9⋊C9C2×D312yes—
38C3⋊AGL(1,ℤ/27)C2×D312yescomplemented
39C3×AGL(1,ℤ/27)—32no—
40C3×AGL(1,ℤ/27)—62no—
41D3×#6875—32no—
42#13090878C22×C312yes—
43#92172⋊C3C22×C312yes—
44#13090876—22no—
45#13090876C22×C312yes—
46#10624472⋊C2—22no—
47C2×C32×C9⋊C9C2×D311yescharacteristic
48C2×C3×#6875—21no—
49C2×C3×#6875C2×D311yescharacteristic, complemented
50C2×#10624683—21no—
51C2×#10624683C22×C311yescharacteristic
52C2×#10624472—21no—
53C2×#10624472—41no—
54C2×C3×C9×C3⋊D3—61no—
55C2×C3×C9×C3⋊D3—91no—
56C2×C3×C9×C3⋊D3—91no—
57C2×C3×C9×C3⋊D3C3×D311yescharacteristic
58C2×C32×C3⋊D9—31no—
59C2×C32×C3⋊D9—31no—
60C9×#1113—94no—
61C3×#66431—34no—
62C2×C3⋊(D27⋊C3)C3×D311yescharacteristic
63C2×C3⋊(D9⋊C9)—31no—
64C2×C3⋊(D9⋊C9)—31no—
65C2×C3⋊(D9⋊C9)—61no—
66C2×C3⋊(D9⋊C9)—61no—
67C2×D3×C27⋊C3—31no—
68C2×D3×C27⋊C3—61no—
69C2×C3×D27⋊C3—31no—
70C2×C3×D27⋊C3—61no—
71C2×D3×C9⋊C9—31no—
72C2×D3×C9⋊C9—181no—
73C2×C3×D9⋊C9—91no—
74C2×C3×D9⋊C9—91no—
75C2×C3×D9⋊C9—181no—
76C2×C3×D9⋊C9—181no—
77D3×D27⋊C3—34no—
78D3×D9⋊C9—94no—
79D3×D9⋊C9—94no—
80C22×#6875—91no—
81C2×#92206C2×C911yescharacteristic, complemented
82C2×AGL(1,ℤ/27)—31no—
83C2×AGL(1,ℤ/27)—61no—
84C2×AGL(1,ℤ/27)—61no—
85C2×AGL(1,ℤ/27)—61no—
86C2×AGL(1,ℤ/27)—61no—
87C2×AGL(1,ℤ/27)—94no—
88C2×AGL(1,ℤ/27)—91no—
89C2×#92172—21no—
90C2×#92172C2×C911yescharacteristic, complemented
91C2×(C3⋊D3)⋊C27—21no—
92C2×(C3⋊D3)⋊C27—61no—
93C2×(C3⋊D3)⋊C27C2×C911yescharacteristic, complemented
94((C3⋊D3)⋊C27)⋊C2C2×C914yescomplemented
95C32×C9⋊C9C22×D311yescharacteristic
96C3×#6875—21no—
97C3×#6875C22×D311yescharacteristic, complemented
98#10624683—21no—
99#10624683C23×C311yescharacteristic
100#10624472—21no—
101#10624472—41no—
102C2×C3×#1113—91no—
103C2×#66431—31no—
104C2×D32×C9—271no—
105C2×D32×C9—271no—
106C2×D32×C9—271no—
107C2×C3×D3×D9—91no—
108C2×C3×D3×D9—91no—
109C22×D27⋊C3—91no—
110C22×D9⋊C9—271no—
111C2×D3×D27—31no—
112C2×C33×C9—61no—
113C2×C33×C9C2×C3×D311yescharacteristic
114C3×C9×C3⋊D3—62no—
115C3×C9×C3⋊D3—92no—
116C3×C9×C3⋊D3—92no—
117C3×C9×C3⋊D3C2×C3×D312yes—
118C32×C3⋊D9—32no—
119C32×C3⋊D9—32no—
120C2×C3×C27⋊C3—21no—
121C2×C3×C27⋊C3—21no—
122C2×C3×C27⋊C3—41no—
123C2×C3×C27⋊C3C2×C3×D311yescharacteristic
124C2×C3×C9⋊C9—21no—
125C2×C3×C9⋊C9—61no—
126C2×C3×C9⋊C9—121no—
127C2×C3×C9⋊C9—121no—
128C2×C3×C9⋊C9—121no—
129C2×C3×C9⋊C9—121no—
130C2×C3×C9⋊C9D3211yescharacteristic
131C3⋊(D27⋊C3)C2×C3×D312yes—
132C3⋊(D9⋊C9)—32no—
133C3⋊(D9⋊C9)—32no—
134C3⋊(D9⋊C9)—62no—
135C3⋊(D9⋊C9)—62no—
136D3×C27⋊C3—32no—
137D3×C27⋊C3—62no—
138C3×D27⋊C3—32no—
139C3×D27⋊C3—62no—
140D3×C9⋊C9—32no—
141D3×C9⋊C9—182no—
142C3×D9⋊C9—92no—
143C3×D9⋊C9—92no—
144C3×D9⋊C9—182no—
145C3×D9⋊C9—182no—
146C2×#6875—31no—
147C2×#6875—61no—
148C2×#6875—92no—
149C2×#6875—121no—
150C2×#6875—121no—
151C2×#6875—121no—
152C2×C32⋊C27—21no—
153C2×C32⋊C27—21no—
154C2×C32⋊C27—41no—
155C2×C32⋊C27—61no—
156C2×C32⋊C27—121no—
157C2×C32⋊C27C22×C911yescharacteristic, complemented
158#92206C22×C912yescomplemented
159AGL(1,ℤ/27)—32no—
160AGL(1,ℤ/27)—62no—
161AGL(1,ℤ/27)—62no—
162AGL(1,ℤ/27)—62no—
163AGL(1,ℤ/27)—62no—
164AGL(1,ℤ/27)—92no—
165#92172—22no—
166#92172C22×C912yescomplemented
167(C3⋊D3)⋊C27—22no—
168(C3⋊D3)⋊C27—62no—
169(C3⋊D3)⋊C27C22×C912yescomplemented
170C2×C32×C3⋊D3—91no—
171C2×C32×C3⋊D3—91no—
172C2×C32×C3⋊D3AGL(1,ℤ/9)11yescharacteristic
173C3×#1113—94no—
174C2×C9×C3⋊D3—21no—
175C2×C9×C3⋊D3—91no—
176C2×C9×C3⋊D3—91no—
177C2×C9×C3⋊D3—181no—
178C2×C9×C3⋊D3—181no—
179C2×C9×C3⋊D3—181no—
180C2×C9×C3⋊D3D3×C911yescharacteristic
181C2×C3×C3⋊D9—31no—
182C2×C3×C3⋊D9—31no—
183C2×C3×C3⋊D9—31no—
184C2×C3×C3⋊D9—31no—
185C2×C3×C3⋊D9—61no—
186C2×C3×C3⋊D9—61no—
187C2×C3×D3×C9—31no—
188C2×C3×D3×C9—91no—
189C2×C3×D3×C9—91no—
190C2×C3×D3×C9—181no—
191C2×C3×D3×C9—181no—
192C2×C3×D3×C9—271no—
193C2×C3×D3×C9—271no—
194C2×C3×D3×C9—271no—
195C2×C3×D3×C9—271no—
196C2×C3×D3×C9—541no—
197C2×C3×D3×C9—541no—
198C2×C32×D9—91no—
199C2×C32×D9—91no—
200C2×C32×D9—181no—
201C2×C32×D9—181no—
202#66431—34no—
203D32×C9—274no—
204D32×C9—274no—
205D32×C9—274no—
206C3×D3×D9—94no—
207C3×D3×D9—94no—
208C22×C27⋊C3—91no—
209C22×C27⋊C3—181no—
210C22×C9⋊C9—91no—
211C2×C3⋊D27D3×C911yescharacteristic, complemented
212C2×D27⋊C3—31no—
213C2×D27⋊C3—61no—
214C2×D27⋊C3—61no—
215C2×D27⋊C3—62no—
216C2×D27⋊C3—94no—
217C2×D27⋊C3—181no—
218C2×D3×C27—31no—
219C2×D3×C27—61no—
220C2×D3×C27—181no—
221C2×C3×D27—31no—
222C2×C3×D27—61no—
223C2×D9⋊C9—91no—
224C2×D9⋊C9—91no—
225C2×D9⋊C9—181no—
226C2×D9⋊C9—181no—
227C2×D9⋊C9—181no—
228C2×D9⋊C9—181no—
229C2×D9⋊C9—181no—
230C2×D9⋊C9—181no—
231C2×D9⋊C9—181no—
232C2×D9⋊C9—181no—
233C2×D9⋊C9—274no—
234D3×D27—34no—
235C33×C9—61no—
236C33×C9C22×C3×D311yescharacteristic
237C3×C27⋊C3—21no—
238C3×C27⋊C3—21no—
239C3×C27⋊C3—41no—
240C3×C27⋊C3C22×C3×D311yescharacteristic
241C3×C9⋊C9—21no—
242C3×C9⋊C9—61no—
243C3×C9⋊C9—121no—
244C3×C9⋊C9—121no—
245C3×C9⋊C9—121no—
246C3×C9⋊C9—121no—
247C3×C9⋊C9C2×D3211yescharacteristic
248#6875—31no—
249#6875—61no—
250#6875—121no—
251#6875—121no—
252#6875—121no—
253C32⋊C27—21no—
254C32⋊C27—21no—
255C32⋊C27—41no—
256C32⋊C27—61no—
257C32⋊C27—121no—
258C32⋊C27C23×C911yescharacteristic, complemented
259C2×#1113—91no—
260C2×C3×D32—271no—
261C2×C3×D32—271no—
262C2×C3×D32—271no—
263C22×D3×C9—811no—
264C22×D3×C9—811no—
265C22×D3×C9—811no—
266C22×C3×D9—271no—
267C2×D3×D9—91no—
268C2×D3×D9—91no—
269C22×D27—91no—
270C2×C34C2×AGL(1,ℤ/9)11yescharacteristic
271C32×C3⋊D3—92no—
272C32×C3⋊D3—92no—
273C32×C3⋊D3C2×AGL(1,ℤ/9)12yes—
274C2×C32×C9—21no—
275C2×C32×C9—21no—
276C2×C32×C9—21no—
277C2×C32×C9—31no—
278C2×C32×C9—31no—
279C2×C32×C9—41no—
280C2×C32×C9—61no—
281C2×C32×C9—61no—
282C2×C32×C9—61no—
283C2×C32×C9—61no—
284C2×C32×C9—121no—
285C2×C32×C9—121no—
286C2×C32×C9—121no—
287C2×C32×C9—121no—
288C2×C32×C9—181no—
289C2×C32×C9—361no—
290C2×C32×C9—361no—
291C2×C32×C9—361no—
292C2×C32×C9C2×D3×C911yescharacteristic
293C2×C32×C9C3×D3211yescharacteristic
294C9×C3⋊D3—22no—
295C9×C3⋊D3—92no—
296C9×C3⋊D3—92no—
297C9×C3⋊D3—182no—
298C9×C3⋊D3—182no—
299C9×C3⋊D3—182no—
300C9×C3⋊D3C2×D3×C912yes—
301C3×C3⋊D9—32no—
302C3×C3⋊D9—32no—
303C3×C3⋊D9—32no—
304C3×C3⋊D9—32no—
305C3×C3⋊D9—62no—
306C3×C3⋊D9—62no—
307C3×D3×C9—32no—
308C3×D3×C9—92no—
309C3×D3×C9—92no—
310C3×D3×C9—182no—
311C3×D3×C9—182no—
312C3×D3×C9—272no—
313C3×D3×C9—272no—
314C3×D3×C9—272no—
315C3×D3×C9—272no—
316C3×D3×C9—542no—
317C3×D3×C9—542no—
318C32×D9—92no—
319C32×D9—92no—
320C32×D9—182no—
321C32×D9—182no—
322C2×C27⋊C3—61no—
323C2×C27⋊C3—61no—
324C2×C27⋊C3—92no—
325C2×C27⋊C3—122no—
326C2×C27⋊C3—121no—
327C2×C27⋊C3—121no—
328C2×C27⋊C3—122no—
329C2×C27⋊C3—121no—
330C2×C27⋊C3—121no—
331C2×C27⋊C3—182no—
332C2×C3×C27—21no—
333C2×C3×C27—21no—
334C2×C3×C27—41no—
335C2×C3×C27—61no—
336C2×C3×C27—121no—
337C2×C3×C27C2×D3×C911yescharacteristic, complemented
338C2×C9⋊C9—21no—
339C2×C9⋊C9—21no—
340C2×C9⋊C9—41no—
341C2×C9⋊C9—61no—
342C2×C9⋊C9—92no—
343C2×C9⋊C9—121no—
344C2×C9⋊C9—121no—
345C2×C9⋊C9—121no—
346C2×C9⋊C9—121no—
347C2×C9⋊C9—121no—
348C2×C9⋊C9—121no—
349C2×C9⋊C9—121no—
350C2×C9⋊C9—121no—
351C2×C9⋊C9((C3⋊D3)⋊C3)⋊C211yescharacteristic
352C3⋊D27C2×D3×C912yescomplemented
353D27⋊C3—32no—
354D27⋊C3—62no—
355D27⋊C3—62no—
356D27⋊C3—64no—
357D27⋊C3—182no—
358D3×C27—32no—
359D3×C27—62no—
360D3×C27—182no—
361C3×D27—32no—
362C3×D27—62no—
363D9⋊C9—92no—
364D9⋊C9—92no—
365D9⋊C9—182no—
366D9⋊C9—182no—
367D9⋊C9—182no—
368D9⋊C9—182no—
369D9⋊C9—182no—
370D9⋊C9—182no—
371D9⋊C9—182no—
372D9⋊C9—182no—
373C2×C3×C3⋊D3—31no—
374C2×C3×C3⋊D3—91no—
375C2×C3×C3⋊D3—91no—
376C2×C3×C3⋊D3—91no—
377C2×C3×C3⋊D3—91no—
378C2×C3×C3⋊D3—181no—
379C2×C3×C3⋊D3—181no—
380C2×C3×C3⋊D3D9⋊C911yescharacteristic
381C2×C32×D3—31no—
382C2×C32×D3—181no—
383C2×C32×D3—271no—
384C2×C32×D3—271no—
385C2×C32×D3—271no—
386C2×C32×D3—271no—
387C2×C32×D3—541no—
388C2×C32×D3—541no—
389#1113—94no—
390C3×D32—274no—
391C3×D32—274no—
392C3×D32—274no—
393C22×C3×C9—91no—
394C22×C3×C9—271no—
395C22×C3×C9—811no—
396C22×C3×C9—811no—
397C2×C3⋊D9—31no—
398C2×C3⋊D9—31no—
399C2×D3×C9—31no—
400C2×D3×C9—61no—
401C2×D3×C9—181no—
402C2×D3×C9—181no—
403C2×D3×C9—271no—
404C2×D3×C9—271no—
405C2×D3×C9—271no—
406C2×D3×C9—271no—
407C2×D3×C9—541no—
408C2×D3×C9—541no—
409C2×D3×C9—541no—
410C2×D3×C9—541no—
411C2×D3×C9—541no—
412C2×D3×C9—541no—
413C2×D3×C9—541no—
414C2×D3×C9—541no—
415C2×D3×C9—541no—
416C2×D3×C9—541no—
417C2×D3×C9—542no—
418C2×D3×C9—541no—
419C2×D3×C9—814no—
420C2×D3×C9—814no—
421C2×D3×C9—814no—
422C2×C3×D9—91no—
423C2×C3×D9—91no—
424C2×C3×D9—91no—
425C2×C3×D9—91no—
426C2×C3×D9—181no—
427C2×C3×D9—181no—
428C2×C3×D9—181no—
429C2×C3×D9—181no—
430C2×C3×D9—182no—
431C2×C3×D9—181no—
432C2×C3×D9—181no—
433C2×C3×D9—182no—
434C2×C3×D9—274no—
435D3×D9—94no—
436D3×D9—94no—
437C22×C27—91no—
438C22×C27—181no—
439C22×C27—541no—
440C2×D27—31no—
441C2×D27—61no—
442C2×D27—94no—
443C2×D27—181no—
444C34C22×AGL(1,ℤ/9)11yescharacteristic
445C32×C9—21no—
446C32×C9—21no—
447C32×C9—21no—
448C32×C9—31no—
449C32×C9—31no—
450C32×C9—41no—
451C32×C9—61no—
452C32×C9—61no—
453C32×C9—61no—
454C32×C9—61no—
455C32×C9—121no—
456C32×C9—121no—
457C32×C9—121no—
458C32×C9—121no—
459C32×C9—181no—
460C32×C9—361no—
461C32×C9—361no—
462C32×C9—361no—
463C32×C9C22×D3×C911yescharacteristic
464C32×C9C2×C3×D3211yescharacteristic
465C27⋊C3—61no—
466C27⋊C3—61no—
467C27⋊C3—122no—
468C27⋊C3—121no—
469C27⋊C3—121no—
470C27⋊C3—122no—
471C27⋊C3—121no—
472C27⋊C3—121no—
473C3×C27—21no—
474C3×C27—21no—
475C3×C27—41no—
476C3×C27—61no—
477C3×C27—121no—
478C3×C27C22×D3×C911yescharacteristic, complemented
479C9⋊C9—21no—
480C9⋊C9—21no—
481C9⋊C9—41no—
482C9⋊C9—61no—
483C9⋊C9—121no—
484C9⋊C9—121no—
485C9⋊C9—121no—
486C9⋊C9—121no—
487C9⋊C9—121no—
488C9⋊C9—121no—
489C9⋊C9—121no—
490C9⋊C9—121no—
491C9⋊C9C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
492C22×C3×D3—811no—
493C22×C3×D3—811no—
494C22×C3×D3—811no—
495C2×D32—271no—
496C2×D32—271no—
497C2×D32—271no—
498C23×C9—2431no—
499C22×D9—271no—
500C2×C33—21no—
501C2×C33—31no—
502C2×C33—61no—
503C2×C33—61no—
504C2×C33—61no—
505C2×C33—121no—
506C2×C33—121no—
507C2×C33C2×D9⋊C911yescharacteristic
508C2×C33D3×AGL(1,ℤ/9)11yescharacteristic
509C3×C3⋊D3—32no—
510C3×C3⋊D3—92no—
511C3×C3⋊D3—92no—
512C3×C3⋊D3—92no—
513C3×C3⋊D3—92no—
514C3×C3⋊D3—182no—
515C3×C3⋊D3—182no—
516C3×C3⋊D3C2×D9⋊C912yes—
517C32×D3—32no—
518C32×D3—182no—
519C32×D3—272no—
520C32×D3—272no—
521C32×D3—272no—
522C32×D3—272no—
523C32×D3—542no—
524C32×D3—542no—
525C2×C3×C9—21no—
526C2×C3×C9—21no—
527C2×C3×C9—21no—
528C2×C3×C9—21no—
529C2×C3×C9—31no—
530C2×C3×C9—41no—
531C2×C3×C9—41no—
532C2×C3×C9—61no—
533C2×C3×C9—62no—
534C2×C3×C9—61no—
535C2×C3×C9—61no—
536C2×C3×C9—61no—
537C2×C3×C9—92no—
538C2×C3×C9—121no—
539C2×C3×C9—121no—
540C2×C3×C9—122no—
541C2×C3×C9—121no—
542C2×C3×C9—122no—
543C2×C3×C9—121no—
544C2×C3×C9—121no—
545C2×C3×C9—121no—
546C2×C3×C9—181no—
547C2×C3×C9—181no—
548C2×C3×C9—181no—
549C2×C3×C9—181no—
550C2×C3×C9—272no—
551C2×C3×C9—361no—
552C2×C3×C9—361no—
553C2×C3×C9—362no—
554C2×C3×C9—361no—
555C2×C3×C9—361no—
556C2×C3×C9—362no—
557C2×C3×C9—361no—
558C2×C3×C9—361no—
559C2×C3×C9—361no—
560C2×C3×C9—812no—
561C2×C3×C9—812no—
562C2×C3×C9D32×C911yescharacteristic
563C2×C3×C9C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
564C3⋊D9—32no—
565C3⋊D9—32no—
566D3×C9—32no—
567D3×C9—62no—
568D3×C9—182no—
569D3×C9—182no—
570D3×C9—272no—
571D3×C9—272no—
572D3×C9—272no—
573D3×C9—272no—
574D3×C9—542no—
575D3×C9—542no—
576D3×C9—542no—
577D3×C9—542no—
578D3×C9—542no—
579D3×C9—542no—
580D3×C9—542no—
581D3×C9—542no—
582D3×C9—542no—
583D3×C9—542no—
584D3×C9—544no—
585D3×C9—542no—
586C3×D9—92no—
587C3×D9—92no—
588C3×D9—92no—
589C3×D9—92no—
590C3×D9—182no—
591C3×D9—182no—
592C3×D9—182no—
593C3×D9—182no—
594C3×D9—182no—
595C3×D9—182no—
596C3×D9—184no—
597C3×D9—184no—
598C2×C27—61no—
599C2×C27—92no—
600C2×C27—121no—
601C2×C27—121no—
602C2×C27—121no—
603C2×C27—182no—
604C2×C27—361no—
605C2×C27—361no—
606C2×C27—542no—
607D27—32no—
608D27—62no—
609D27—182no—
610C22×C32—91no—
611C22×C32—811no—
612C22×C32—811no—
613C2×C3⋊D3—91no—
614C2×C3⋊D3—91no—
615C2×C3⋊D3AGL(1,ℤ/27)11yescharacteristic, complemented
616C2×C3×D3—31no—
617C2×C3×D3—91no—
618C2×C3×D3—91no—
619C2×C3×D3—181no—
620C2×C3×D3—181no—
621C2×C3×D3—271no—
622C2×C3×D3—271no—
623C2×C3×D3—271no—
624C2×C3×D3—271no—
625C2×C3×D3—271no—
626C2×C3×D3—271no—
627C2×C3×D3—271no—
628C2×C3×D3—271no—
629C2×C3×D3—541no—
630C2×C3×D3—541no—
631C2×C3×D3—541no—
632C2×C3×D3—541no—
633C2×C3×D3—541no—
634C2×C3×D3—541no—
635C2×C3×D3—541no—
636C2×C3×D3—541no—
637C2×C3×D3—541no—
638C2×C3×D3—541no—
639C2×C3×D3—541no—
640C2×C3×D3—541no—
641C2×C3×D3—814no—
642C2×C3×D3—814no—
643C2×C3×D3—814no—
644D32—274no—
645D32—274no—
646D32—274no—
647C22×C9—91no—
648C22×C9—181no—
649C22×C9—811no—
650C22×C9—811no—
651C22×C9—1621no—
652C22×C9—1621no—
653C22×C9—1621no—
654C22×C9—2434no—
655C2×D9—91no—
656C2×D9—91no—
657C2×D9—181no—
658C2×D9—181no—
659C2×D9—274no—
660C33—21no—
661C33—31no—
662C33—61no—
663C33—61no—
664C33—61no—
665C33—121no—
666C33—121no—
667C33C22×D9⋊C911yescharacteristic
668C33C2×D3×AGL(1,ℤ/9)11yescharacteristic
669C3×C9—21no—
670C3×C9—21no—
671C3×C9—21no—
672C3×C9—21no—
673C3×C9—31no—
674C3×C9—41no—
675C3×C9—41no—
676C3×C9—61no—
677C3×C9—62no—
678C3×C9—61no—
679C3×C9—61no—
680C3×C9—61no—
681C3×C9—121no—
682C3×C9—121no—
683C3×C9—122no—
684C3×C9—121no—
685C3×C9—122no—
686C3×C9—121no—
687C3×C9—121no—
688C3×C9—121no—
689C3×C9—181no—
690C3×C9—181no—
691C3×C9—181no—
692C3×C9—181no—
693C3×C9—361no—
694C3×C9—361no—
695C3×C9—362no—
696C3×C9—361no—
697C3×C9—361no—
698C3×C9—362no—
699C3×C9—361no—
700C3×C9—361no—
701C3×C9—361no—
702C3×C9C2×D32×C911yescharacteristic
703C3×C9C2×C3×((C3⋊D3)⋊C3)⋊C211yescharacteristic
704C27—61no—
705C27—121no—
706C27—121no—
707C27—121no—
708C27—361no—
709C27—361no—
710C23×C3—2431no—
711C22×D3—811no—
712C22×D3—811no—
713C22×D3—811no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—31no—
718C2×C32—31no—
719C2×C32—41no—
720C2×C32—61no—
721C2×C32—61no—
722C2×C32—61no—
723C2×C32—61no—
724C2×C32—61no—
725C2×C32—61no—
726C2×C32—92no—
727C2×C32—121no—
728C2×C32—121no—
729C2×C32—121no—
730C2×C32—121no—
731C2×C32—121no—
732C2×C32—121no—
733C2×C32—121no—
734C2×C32—121no—
735C2×C32—121no—
736C2×C32—812no—
737C2×C32—812no—
738C2×C32C2×AGL(1,ℤ/27)11yescharacteristic, complemented
739C2×C32D3×D9⋊C911yescharacteristic
740C2×C32(((C3⋊D3)⋊C9)⋊C2)⋊C311yescharacteristic
741C3⋊D3—92no—
742C3⋊D3—92no—
743C3⋊D3C2×AGL(1,ℤ/27)12yescomplemented
744C3×D3—32no—
745C3×D3—92no—
746C3×D3—92no—
747C3×D3—182no—
748C3×D3—182no—
749C3×D3—272no—
750C3×D3—272no—
751C3×D3—272no—
752C3×D3—272no—
753C3×D3—272no—
754C3×D3—272no—
755C3×D3—272no—
756C3×D3—272no—
757C3×D3—542no—
758C3×D3—542no—
759C3×D3—542no—
760C3×D3—542no—
761C3×D3—542no—
762C3×D3—542no—
763C3×D3—542no—
764C3×D3—542no—
765C3×D3—542no—
766C3×D3—542no—
767C3×D3—542no—
768C3×D3—542no—
769C2×C9—21no—
770C2×C9—21no—
771C2×C9—41no—
772C2×C9—92no—
773C2×C9—121no—
774C2×C9—121no—
775C2×C9—181no—
776C2×C9—181no—
777C2×C9—182no—
778C2×C9—361no—
779C2×C9—361no—
780C2×C9—812no—
781C2×C9—812no—
782C2×C9—1622no—
783C2×C9—1622no—
784C2×C9—1622no—
785C2×C9C9×((C3⋊D3)⋊C3)⋊C211yescharacteristic
786D9—92no—
787D9—92no—
788D9—182no—
789D9—182no—
790C22×C3—91no—
791C22×C3—271no—
792C22×C3—811no—
793C22×C3—811no—
794C22×C3—811no—
795C22×C3—811no—
796C22×C3—1621no—
797C22×C3—1621no—
798C22×C3—2434no—
799C2×D3—31no—
800C2×D3—181no—
801C2×D3—271no—
802C2×D3—271no—
803C2×D3—271no—
804C2×D3—271no—
805C2×D3—541no—
806C2×D3—541no—
807C2×D3—814no—
808C2×D3—814no—
809C2×D3—814no—
810C32—21no—
811C32—21no—
812C32—21no—
813C32—31no—
814C32—31no—
815C32—41no—
816C32—61no—
817C32—61no—
818C32—61no—
819C32—61no—
820C32—61no—
821C32—61no—
822C32—121no—
823C32—121no—
824C32—121no—
825C32—121no—
826C32—121no—
827C32—121no—
828C32—121no—
829C32—121no—
830C32—121no—
831C32C22×AGL(1,ℤ/27)11yescharacteristic, complemented
832C32C2×D3×D9⋊C911yescharacteristic
833C32C2×(((C3⋊D3)⋊C9)⋊C2)⋊C311yescharacteristic
834C9—21no—
835C9—21no—
836C9—41no—
837C9—121no—
838C9—121no—
839C9—181no—
840C9—181no—
841C9—361no—
842C9—361no—
843C9C2×C9×((C3⋊D3)⋊C3)⋊C211yescharacteristic
844C23—2431noSylow
845C2×C3—21no—
846C2×C3—31no—
847C2×C3—61no—
848C2×C3—61no—
849C2×C3—61no—
850C2×C3—61no—
851C2×C3—92no—
852C2×C3—121no—
853C2×C3—272no—
854C2×C3—812no—
855C2×C3—812no—
856C2×C3—812no—
857C2×C3—812no—
858C2×C3—1622no—
859C2×C3—1622no—
860C2×C3D3×AGL(1,ℤ/27)11yescharacteristic
861C2×C3#7222186111yescharacteristic
862D3—32no—
863D3—182no—
864D3—272no—
865D3—272no—
866D3—272no—
867D3—272no—
868D3—542no—
869D3—542no—
870C22—91no—
871C22—811no—
872C22—811no—
873C22—2434no—
874C3—21no—
875C3—31no—
876C3—61no—
877C3—61no—
878C3—61no—
879C3—61no—
880C3—121no—
881C3C2×D3×AGL(1,ℤ/27)11yescharacteristic
882C3C2×#7222186111yescharacteristic
883C2—92no—
884C2—812no—
885C2—812no—
886C2#7222186211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#72221862
commutator, hypocenterC32⋊C27C23×C9
FrattiniC32×C9C2×C3×D32
FittingC2×#14550484C22
socleC2×C32D3×D9⋊C9
prime radicalC2×#72221850C3
cosocle#10624683C23×C3
LCSG ▷ C32⋊C27
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C2×#72221838C2semidirect
6. C2×#72221832C2semidirect
10. C2×#72221821C2semidirect
14. C2×#14550484C22semidirect
16. C2×C3⋊AGL(1,ℤ/27)D3semidirect
18. #72221862C2direct (N × H)
21. #72221838C22semidirect
22. #72221832C22semidirect
23. #72221821C22semidirect
27. #14550484C23semidirect
34. C2×((C3⋊D3)⋊C27)⋊C2C9semidirect
38. C3⋊AGL(1,ℤ/27)C2×D3semidirect
49. C2×C3×#6875C2×D3semidirect
81. C2×#92206C2×C9semidirect
90. C2×#92172C2×C9semidirect
93. C2×(C3⋊D3)⋊C27C2×C9semidirect
94. ((C3⋊D3)⋊C27)⋊C2C2×C9semidirect
97. C3×#6875C22×D3semidirect
157. C2×C32⋊C27C22×C9semidirect
158. #92206C22×C9semidirect
166. #92172C22×C9semidirect
169. (C3⋊D3)⋊C27C22×C9semidirect
211. C2×C3⋊D27D3×C9semidirect
258. C32⋊C27C23×C9semidirect
337. C2×C3×C27C2×D3×C9semidirect
352. C3⋊D27C2×D3×C9semidirect
478. C3×C27C22×D3×C9semidirect
615. C2×C3⋊D3AGL(1,ℤ/27)semidirect
738. C2×C32C2×AGL(1,ℤ/27)semidirect
743. C3⋊D3C2×AGL(1,ℤ/27)semidirect
831. C32C22×AGL(1,ℤ/27)semidirect
886. C2#72221862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#722218593
C2×#722218503
C2×#722218382
C2×#722218322
C2×#722218212
C2×D3×AGL(1,ℤ/27)3
#722218622