Finite Group Databasebeta

← #72243588

Subgroups — #72243588

Order 8748.

762 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 90 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
1#72243550C211yesmaximal, characteristic, complemented
2#72243550C211yesmaximal, characteristic, complemented
3#72243525C211yesmaximal, characteristic, complemented
4#72243331C311yesmaximal, characteristic, complemented
5D9×D9⋊C9C311yesmaximal, characteristic, complemented
6D9×D9⋊C9C311yesmaximal, characteristic, complemented
7D3×#92264—31nomaximal
8D3×#92264—31nomaximal
9C3×#92265⋊C2C311yesmaximal, characteristic
10#14552545C2211yescharacteristic, complemented, Sylow
11C3×#92314C2×C311yescharacteristic
12C3×#92265C2×C311yescharacteristic
13C3×#92265C2×C311yescharacteristic
14D3×#6896—31no—
15D3×#6896—31no—
16C3⋊#92264—31no—
17C3⋊#92264—31no—
18C3×#92264D311yescharacteristic
19C3×#92264D311yescharacteristic
20#13090669—61no—
21(D9⋊C9)⋊C9—21no—
22(D9⋊C9)⋊C9—21no—
23(D9⋊C9)⋊C9—21no—
24(D9⋊C9)⋊C9—21no—
25(C3×AGL(1,ℤ/9))⋊C9—21no—
26(C3×AGL(1,ℤ/9))⋊C9—21no—
27#13090629C2×C311yescharacteristic, complemented
28#13090628—21no—
29#13090628—21no—
30#13090628C2×C311yescharacteristic, complemented
31#13090628C2×C311yescharacteristic, complemented
32C9×D9⋊C9C2×C311yescharacteristic, complemented
33C9×D9⋊C9C2×C311yescharacteristic, complemented
34#13090615C2×C311yescharacteristic, complemented
35#13090615C2×C311yescharacteristic, complemented
36D9×C9⋊C9C2×C311yescharacteristic, complemented
37D9×C9⋊C9C2×C311yescharacteristic, complemented
38D32×3−1+2—91no—
39C3×D3×AGL(1,ℤ/9)—31no—
40C3×D3×AGL(1,ℤ/9)—31no—
41C2×#92264—91no—
42C2×#92264—91no—
43#92265⋊C2—31no—
44D3×D9⋊C9—31no—
45D3×D9⋊C9—31no—
46D3×D9⋊C9—31no—
47D3×D9⋊C9—31no—
48D3×C9×D9—31no—
49D3×C9×D9—31no—
50C3×D92C3211yescharacteristic
51C3×#6900C22×C311yescharacteristic
52C3×#6896C2×D311yescharacteristic
53C3×#6896C2×D311yescharacteristic
54#10624575—41no—
55#10624575—41no—
56#10624572—41no—
57#10624567—21no—
58#10624565—41no—
59#10624561—21no—
60#10624561—21no—
61#10624561—21no—
62#10624561—21no—
63#10624560—21no—
64#10624560—21no—
65#10624550—21no—
66#10624550—21no—
67#10624550C22×C311yescharacteristic, complemented
68C9×C9⋊C9C22×C311yescharacteristic, complemented
69C9×C9⋊C9C22×C311yescharacteristic, complemented
70C3⋊D3×3−1+2—91no—
71C3×C3⋊AGL(1,ℤ/9)—31no—
72C3×C3⋊AGL(1,ℤ/9)—31no—
73C3×C3⋊AGL(1,ℤ/9)—61no—
74C3×D3×3−1+2—31no—
75C3×D3×3−1+2—31no—
76C3×D3×3−1+2—31no—
77C3×D3×3−1+2—31no—
78C32×AGL(1,ℤ/9)C3×D311yescharacteristic
79C32×AGL(1,ℤ/9)C3×D311yescharacteristic
80C2×#6896—91no—
81C2×#6896—91no—
82#92314—31no—
83C3⋊(D9⋊C9)—31no—
84C3⋊(D9⋊C9)—31no—
85C3⋊(D9⋊C9)—31no—
86C3⋊(D9⋊C9)—31no—
87C3×C9⋊D9C2×C3211yescharacteristic
88C9×C3⋊D9—31no—
89C9×C3⋊D9—31no—
90#92265—31no—
91#92265—31no—
92#92265—61no—
93#92265—61no—
94#92264—31no—
95#92264—31no—
96#92264—61no—
97#92264—61no—
98#92264—91no—
99#92264—91no—
100#92264—181no—
101#92264—181no—
102D3×C9⋊C9—31no—
103D3×C9⋊C9—31no—
104D3×C9⋊C9—31no—
105D3×C9⋊C9—31no—
106D3×C9⋊C9—61no—
107D3×C9⋊C9—61no—
108D3×C9⋊C9—61no—
109D3×C9⋊C9—61no—
110D3×C9⋊C9—61no—
111D3×C9⋊C9—61no—
112C3×D9⋊C9—21no—
113C3×D9⋊C9—21no—
114C3×D9⋊C9—21no—
115C3×D9⋊C9—21no—
116C3×D9⋊C9—21no—
117C3×D9⋊C9—21no—
118C3×D9⋊C9C3×D311yescharacteristic
119C3×D9⋊C9C3×D311yescharacteristic
120C3×D9⋊C9C3×D311yescharacteristic
121C3×D9⋊C9C3×D311yescharacteristic
122D3×C32⋊C9—61no—
123D3×C32⋊C9—61no—
124D3×C92—31no—
125D3×C92—31no—
126C3×C9×D9—21no—
127C3×C9×D9—21no—
128C3×C9×D9C3×D311yescharacteristic
129C3×C9×D9C3×D311yescharacteristic
130C3×C9×D9C2×C3211yescharacteristic
131C3×C9×D9C2×C3211yescharacteristic
132#92158—61no—
133#92158—61no—
134#92158—61no—
135C32×D32—91no—
136C2×D3×3−1+2—271no—
137C2×D3×3−1+2—271no—
138C2×C3×AGL(1,ℤ/9)—91no—
139C2×C3×AGL(1,ℤ/9)—91no—
140D3×AGL(1,ℤ/9)—91no—
141D3×AGL(1,ℤ/9)—91no—
142D32×C9—91no—
143D32×C9—91no—
144D32×C9—91no—
145C3×D3×D9—31no—
146C3×D3×D9—31no—
147C2×D9⋊C9—91no—
148C2×D9⋊C9—91no—
149C2×D9⋊C9—91no—
150C2×D9⋊C9—91no—
151C2×C9×D9—91no—
152C2×C9×D9—91no—
153D923−1+211yescharacteristic, complemented
154C32×3−1+2—21no—
155C32×3−1+2D3211yescharacteristic
156C32×3−1+2C2×C3×D311yescharacteristic
157C32×3−1+2C2×C3×D311yescharacteristic
158#6900—31no—
159#6900—61no—
160#6900—61no—
161#6900—121no—
162#6896—31no—
163#6896—31no—
164#6896—61no—
165#6896—61no—
166#6896—61no—
167#6896—121no—
168#6896—121no—
169#6896—121no—
170C3×C9⋊C9—21no—
171C3×C9⋊C9—21no—
172C3×C9⋊C9—21no—
173C3×C9⋊C9—21no—
174C3×C9⋊C9—21no—
175C3×C9⋊C9—21no—
176C3×C9⋊C9—21no—
177C3×C9⋊C9—21no—
178C3×C9⋊C9—21no—
179C3×C9⋊C9—21no—
180C3×C9⋊C9—21no—
181C3×C9⋊C9—21no—
182C3×C9⋊C9—41no—
183C3×C9⋊C9—41no—
184C3×C9⋊C9—41no—
185C3×C9⋊C9—41no—
186C3×C9⋊C9C2×C3×D311yescharacteristic
187C3×C9⋊C9C2×C3×D311yescharacteristic
188C3×C9⋊C9C2×C3×D311yescharacteristic
189C3×C9⋊C9C2×C3×D311yescharacteristic
190C3×C32⋊C9—21no—
191C3×C32⋊C9—21no—
192C3×C32⋊C9—41no—
193C3×C92—21no—
194C3×C92—21no—
195C3×C92C2×C3×D311yescharacteristic
196C3×C92C2×C3×D311yescharacteristic
197C3×C92C22×C3211yescharacteristic
198#6855—21no—
199#6855—21no—
200#6855—21no—
201#6855—41no—
202#6855—41no—
203#6855—41no—
204#6855—41no—
205#6855—41no—
206#6855—41no—
207#6855—41no—
208#6855—41no—
209#6855—41no—
210#6855—41no—
211#6855—41no—
212#6855—41no—
213#6855—41no—
214#6855—41no—
215#6855—41no—
216C32×C3⋊D3—91no—
217C33×D3—31no—
218C33×D3—31no—
219C2×C3×3−1+2—91no—
220C2×C3×3−1+2—91no—
221C2×C3×3−1+2—91no—
222C2×C3×3−1+2—91no—
223C3⋊AGL(1,ℤ/9)—91no—
224C3⋊AGL(1,ℤ/9)—91no—
225C3⋊AGL(1,ℤ/9)—181no—
226C9×C3⋊D3—91no—
227C9×C3⋊D3—91no—
228C9×C3⋊D3—91no—
229C3×C3⋊D9—31no—
230C3×C3⋊D9—31no—
231C3×C3⋊D9—61no—
232D3×3−1+2—91no—
233D3×3−1+2—91no—
234D3×3−1+2—181no—
235D3×3−1+2—181no—
236D3×3−1+2—181no—
237D3×3−1+2—181no—
238D3×3−1+2—181no—
239D3×3−1+2—181no—
240D3×3−1+2—271no—
241D3×3−1+2—271no—
242D3×3−1+2—541no—
243C3×AGL(1,ℤ/9)—31no—
244C3×AGL(1,ℤ/9)—31no—
245C3×AGL(1,ℤ/9)—31no—
246C3×AGL(1,ℤ/9)—61no—
247C3×AGL(1,ℤ/9)—61no—
248C3×AGL(1,ℤ/9)—61no—
249C3×AGL(1,ℤ/9)—91no—
250C3×AGL(1,ℤ/9)—91no—
251C3×AGL(1,ℤ/9)—181no—
252C3×AGL(1,ℤ/9)—181no—
253C3×AGL(1,ℤ/9)—541no—
254C3×D3×C9—31no—
255C3×D3×C9—31no—
256C3×D3×C9—31no—
257C3×D3×C9—31no—
258C3×D3×C9—31no—
259C3×D3×C9—31no—
260C3×D3×C9—31no—
261C3×D3×C9—31no—
262C3×D3×C9—61no—
263C3×D3×C9—61no—
264C3×D3×C9—61no—
265C3×D3×C9—61no—
266C3×D3×C9—61no—
267C3×D3×C9—61no—
268C3×D3×C9—61no—
269C3×D3×C9—61no—
270C32×D9C32×D311yescharacteristic
271C32×D9C32×D311yescharacteristic
272C2×C9⋊C9—91no—
273C2×C9⋊C9—91no—
274C2×C9⋊C9—91no—
275C2×C9⋊C9—91no—
276C2×C9⋊C9—181no—
277C2×C9⋊C9—181no—
278C2×C9⋊C9—181no—
279C2×C9⋊C9—181no—
280C2×C9⋊C9—181no—
281C2×C9⋊C9—181no—
282C2×C32⋊C9—181no—
283C2×C32⋊C9—181no—
284C2×C92—91no—
285C2×C92—91no—
286C9⋊D9C2×3−1+211yescharacteristic, complemented
287D9⋊C9—21no—
288D9⋊C9—21no—
289D9⋊C9—31no—
290D9⋊C9—31no—
291D9⋊C9—61no—
292D9⋊C9—61no—
293D9⋊C9—61no—
294D9⋊C9—61no—
295D9⋊C9—61no—
296D9⋊C9—61no—
297D9⋊C9—91no—
298D9⋊C9—91no—
299D9⋊C9—91no—
300D9⋊C9—91no—
301D9⋊C9—181no—
302D9⋊C9—181no—
303D9⋊C9—181no—
304D9⋊C9—181no—
305D9⋊C9AGL(1,ℤ/9)11yescharacteristic, complemented
306D9⋊C9AGL(1,ℤ/9)11yescharacteristic, complemented
307C9×D9—21no—
308C9×D9—21no—
309C9×D9—31no—
310C9×D9—61no—
311C9×D9—61no—
312C9×D9—61no—
313C9×D9—91no—
314C9×D9—91no—
315C9×D9—181no—
316C9×D9—181no—
317C9×D9C2×3−1+211yescharacteristic, complemented
318C9×D9C2×3−1+211yescharacteristic, complemented
319C2×C32×D3—271no—
320C2×C32×D3—271no—
321C3×D32—91no—
322C3×D32—271no—
323C22×3−1+2—811no—
324C2×AGL(1,ℤ/9)—271no—
325C2×AGL(1,ℤ/9)—271no—
326C2×D3×C9—271no—
327C2×D3×C9—271no—
328C2×D3×C9—271no—
329C2×D3×C9—271no—
330C2×D3×C9—271no—
331C2×D3×C9—271no—
332C2×C3×D9—91no—
333C2×C3×D9—91no—
334D3×D9—31no—
335D3×D9—31no—
336C34C3×D3211yescharacteristic
337C3×3−1+2—31no—
338C3×3−1+2—31no—
339C3×3−1+2—31no—
340C3×3−1+2—61no—
341C3×3−1+2—61no—
342C3×3−1+2—61no—
343C3×3−1+2—61no—
344C3×3−1+2—61no—
345C3×3−1+2—61no—
346C3×3−1+2—61no—
347C3×3−1+2—61no—
348C3×3−1+2—61no—
349C3×3−1+2—61no—
350C3×3−1+2—121no—
351C3×3−1+2—121no—
352C3×3−1+2—121no—
353C3×3−1+2—121no—
354C3×3−1+2—121no—
355C3×3−1+2—181no—
356C3×3−1+2—361no—
357C3×3−1+2—361no—
358C32×C9—21no—
359C32×C9—21no—
360C32×C9—21no—
361C32×C9—21no—
362C32×C9—21no—
363C32×C9—21no—
364C32×C9—21no—
365C32×C9—21no—
366C32×C9—21no—
367C32×C9—41no—
368C32×C9—41no—
369C32×C9—41no—
370C32×C9—41no—
371C32×C9C3×D3211yescharacteristic
372C32×C9C3×D3211yescharacteristic
373C32×C9C3×D3211yescharacteristic
374C32×C9C2×C32×D311yescharacteristic
375C32×C9C2×C32×D311yescharacteristic
376C9⋊C9—21no—
377C9⋊C9—21no—
378C9⋊C9—21no—
379C9⋊C9—21no—
380C9⋊C9—31no—
381C9⋊C9—31no—
382C9⋊C9—41no—
383C9⋊C9—41no—
384C9⋊C9—61no—
385C9⋊C9—61no—
386C9⋊C9—61no—
387C9⋊C9—61no—
388C9⋊C9—61no—
389C9⋊C9—61no—
390C9⋊C9—61no—
391C9⋊C9—121no—
392C9⋊C9—121no—
393C9⋊C9—121no—
394C9⋊C9—121no—
395C9⋊C9—121no—
396C9⋊C9—121no—
397C9⋊C9—121no—
398C9⋊C9—121no—
399C9⋊C9—121no—
400C9⋊C9—121no—
401C9⋊C9—121no—
402C9⋊C9—121no—
403C9⋊C9—121no—
404C9⋊C9—121no—
405C9⋊C9—122no—
406C9⋊C9—121no—
407C9⋊C9—121no—
408C9⋊C9—121no—
409C9⋊C9—121no—
410C9⋊C9—121no—
411C9⋊C9—121no—
412C9⋊C9—361no—
413C9⋊C9—361no—
414C9⋊C9—361no—
415C9⋊C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
416C9⋊C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
417C32⋊C9—121no—
418C32⋊C9—121no—
419C32⋊C9—121no—
420C32⋊C9—121no—
421C32⋊C9—361no—
422C92—21no—
423C92—21no—
424C92—31no—
425C92—41no—
426C92—61no—
427C92—61no—
428C92—61no—
429C92—61no—
430C92—121no—
431C92—121no—
432C92—121no—
433C92C22×3−1+211yescharacteristic, complemented
434C2×C33—91no—
435C2×C33—91no—
436C3×C3⋊D3—91no—
437C3×C3⋊D3—271no—
438C32×D3—31no—
439C32×D3—31no—
440C32×D3—91no—
441C32×D3—91no—
442C32×D3—91no—
443C32×D3—181no—
444C32×D3—181no—
445C32×D3—181no—
446C32×D3—271no—
447C32×D3—271no—
448C32×D3—541no—
449C2×3−1+2—271no—
450C2×3−1+2—271no—
451C2×3−1+2—271no—
452C2×3−1+2—541no—
453C2×3−1+2—541no—
454C2×3−1+2—541no—
455C2×3−1+2—541no—
456C2×3−1+2—541no—
457C2×3−1+2—811no—
458C2×C3×C9—91no—
459C2×C3×C9—91no—
460C2×C3×C9—91no—
461C2×C3×C9—91no—
462C2×C3×C9—91no—
463C2×C3×C9—91no—
464C2×C3×C9—91no—
465C2×C3×C9—91no—
466C2×C3×C9—181no—
467C2×C3×C9—181no—
468C2×C3×C9—181no—
469C2×C3×C9—181no—
470C2×C3×C9—181no—
471C2×C3×C9—181no—
472C2×C3×C9—181no—
473C2×C3×C9—181no—
474C3⋊D9—31no—
475C3⋊D9—31no—
476C3⋊D9—61no—
477AGL(1,ℤ/9)—91no—
478AGL(1,ℤ/9)—91no—
479AGL(1,ℤ/9)—271no—
480AGL(1,ℤ/9)—271no—
481AGL(1,ℤ/9)—541no—
482AGL(1,ℤ/9)—541no—
483AGL(1,ℤ/9)—542no—
484AGL(1,ℤ/9)—541no—
485D3×C9—31no—
486D3×C9—31no—
487D3×C9—31no—
488D3×C9—31no—
489D3×C9—61no—
490D3×C9—61no—
491D3×C9—61no—
492D3×C9—61no—
493D3×C9—91no—
494D3×C9—181no—
495D3×C9—181no—
496D3×C9—181no—
497D3×C9—181no—
498D3×C9—181no—
499D3×C9—181no—
500D3×C9—181no—
501D3×C9—181no—
502D3×C9—181no—
503D3×C9—181no—
504D3×C9—181no—
505D3×C9—271no—
506D3×C9—271no—
507D3×C9—271no—
508D3×C9—271no—
509D3×C9—271no—
510D3×C9—271no—
511D3×C9—541no—
512D3×C9—541no—
513D3×C9—541no—
514C3×D9—21no—
515C3×D9—21no—
516C3×D9—91no—
517C3×D9—91no—
518C3×D9—181no—
519C3×D9—181no—
520C3×D9—541no—
521C3×D9C3×AGL(1,ℤ/9)11yescharacteristic
522C3×D9C3×AGL(1,ℤ/9)11yescharacteristic
523C3×D9D3×3−1+211yescharacteristic
524C3×D9D3×3−1+211yescharacteristic
525C22×C32—811no—
526C2×C3×D3—271no—
527C2×C3×D3—271no—
528C2×C3×D3—811no—
529C2×C3×D3—811no—
530D32—91no—
531C22×C9—811no—
532C22×C9—811no—
533C22×C9—811no—
534C2×D9—91no—
535C2×D9—91no—
536C33—31no—
537C33—31no—
538C33—61no—
539C33—61no—
540C33—61no—
541C33—121no—
542C33—121no—
543C33C32×D3211yescharacteristic
5443−1+2—91no—
5453−1+2—91no—
5463−1+2—181no—
5473−1+2—181no—
5483−1+2—181no—
5493−1+2—181no—
5503−1+2—182no—
5513−1+2—361no—
5523−1+2—361no—
5533−1+2—361no—
5543−1+2—361no—
5553−1+2—361no—
5563−1+2—361no—
5573−1+2—361no—
5583−1+2—363no—
559C3×C9—21no—
560C3×C9—21no—
561C3×C9—21no—
562C3×C9—21no—
563C3×C9—21no—
564C3×C9—21no—
565C3×C9—21no—
566C3×C9—21no—
567C3×C9—21no—
568C3×C9—21no—
569C3×C9—21no—
570C3×C9—31no—
571C3×C9—41no—
572C3×C9—41no—
573C3×C9—41no—
574C3×C9—41no—
575C3×C9—41no—
576C3×C9—61no—
577C3×C9—61no—
578C3×C9—61no—
579C3×C9—61no—
580C3×C9—61no—
581C3×C9—61no—
582C3×C9—61no—
583C3×C9—61no—
584C3×C9—61no—
585C3×C9—61no—
586C3×C9—61no—
587C3×C9—61no—
588C3×C9—61no—
589C3×C9—121no—
590C3×C9—121no—
591C3×C9—121no—
592C3×C9—121no—
593C3×C9—121no—
594C3×C9—121no—
595C3×C9—121no—
596C3×C9—121no—
597C3×C9—121no—
598C3×C9—121no—
599C3×C9—121no—
600C3×C9—121no—
601C3×C9—121no—
602C3×C9—121no—
603C3×C9—121no—
604C3×C9—121no—
605C3×C9—121no—
606C3×C9—121no—
607C3×C9—121no—
608C3×C9—121no—
609C3×C9—121no—
610C3×C9—121no—
611C3×C9—121no—
612C3×C9—121no—
613C3×C9—121no—
614C3×C9—121no—
615C3×C9—121no—
616C3×C9—121no—
617C3×C9—121no—
618C3×C9—121no—
619C3×C9—121no—
620C3×C9—121no—
621C3×C9—121no—
622C3×C9D3×AGL(1,ℤ/9)11yescharacteristic
623C3×C9D3×AGL(1,ℤ/9)11yescharacteristic
624C3×C9C2×C3×AGL(1,ℤ/9)11yescharacteristic
625C3×C9C2×C3×AGL(1,ℤ/9)11yescharacteristic
626C3×C9C2×D3×3−1+211yescharacteristic
627C3×C9C2×D3×3−1+211yescharacteristic
628C2×C32—91no—
629C2×C32—91no—
630C2×C32—271no—
631C2×C32—271no—
632C2×C32—271no—
633C2×C32—271no—
634C2×C32—541no—
635C2×C32—541no—
636C2×C32—811no—
637C3⋊D3—91no—
638C3×D3—31no—
639C3×D3—31no—
640C3×D3—31no—
641C3×D3—31no—
642C3×D3—61no—
643C3×D3—61no—
644C3×D3—271no—
645C3×D3—271no—
646C3×D3—541no—
647C3×D3—541no—
648C3×D3—541no—
649C3×D3—811no—
650C3×D3—811no—
651C3×D3—1621no—
652C2×C9—91no—
653C2×C9—91no—
654C2×C9—91no—
655C2×C9—91no—
656C2×C9—181no—
657C2×C9—181no—
658C2×C9—181no—
659C2×C9—181no—
660C2×C9—271no—
661C2×C9—271no—
662C2×C9—271no—
663C2×C9—541no—
664C2×C9—541no—
665C2×C9—541no—
666C2×C9—541no—
667C2×C9—541no—
668C2×C9—541no—
669C2×C9—541no—
670C2×C9—541no—
671C2×C9—541no—
672C2×C9—811no—
673C2×C9—811no—
674C2×C9—811no—
675D9—91no—
676D9—91no—
677D9—181no—
678D9—181no—
679D9—541no—
680D9#9226411yescharacteristic, complemented
681D9#9226411yescharacteristic, complemented
682C22×C3—811no—
683C22×C3—2431no—
684C2×D3—271no—
685C2×D3—271no—
686C32—21no—
687C32—21no—
688C32—21no—
689C32—41no—
690C32—181no—
691C32—181no—
692C32—181no—
693C32—361no—
694C32—361no—
695C32—361no—
696C32—361no—
697C32C3×D3×AGL(1,ℤ/9)11yescharacteristic
698C32C3×D3×AGL(1,ℤ/9)11yescharacteristic
699C32D32×3−1+211yescharacteristic
700C9—21no—
701C9—21no—
702C9—21no—
703C9—21no—
704C9—31no—
705C9—31no—
706C9—41no—
707C9—41no—
708C9—61no—
709C9—61no—
710C9—61no—
711C9—121no—
712C9—121no—
713C9—121no—
714C9—121no—
715C9—121no—
716C9—181no—
717C9—181no—
718C9—181no—
719C9—361no—
720C9—361no—
721C9—361no—
722C9—361no—
723C9—361no—
724C9—361no—
725C9—361no—
726C9—361no—
727C9C2×#9226411yescharacteristic, complemented
728C9C2×#9226411yescharacteristic, complemented
729C2×C3—91no—
730C2×C3—91no—
731C2×C3—91no—
732C2×C3—91no—
733C2×C3—181no—
734C2×C3—181no—
735C2×C3—811no—
736C2×C3—811no—
737C2×C3—811no—
738C2×C3—2431no—
739D3—31no—
740D3—31no—
741D3—271no—
742D3—271no—
743D3—541no—
744C22—811noSylow
745C3—21no—
746C3—21no—
747C3—21no—
748C3—41no—
749C3—1081no—
750C3AGL(1,ℤ/9)211yescharacteristic
751C3D3×#9226411yescharacteristic
752C3D3×#9226411yescharacteristic
753C2—91no—
754C2—91no—
755C2—811no—
subgroupG/H
center, hypercenterC3AGL(1,ℤ/9)2
commutator, cosocleC3×C92C22×C32
Frattini, socleC33C32×D32
Fitting#14552545C22
prime radicalC3×#92265⋊C2C3
hypocenterC92C22×3−1+2
LCSG ▷ C3×C92 ▷ C92
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. #72243550C2semidirect
2. #72243550C2semidirect
3. #72243525C2semidirect
4. #72243331C3semidirect
5. D9×D9⋊C9C3semidirect
6. D9×D9⋊C9C3semidirect
10. #14552545C22semidirect
27. #13090629C2×C3semidirect
30. #13090628C2×C3semidirect
31. #13090628C2×C3semidirect
32. C9×D9⋊C9C2×C3semidirect
33. C9×D9⋊C9C2×C3semidirect
34. #13090615C2×C3semidirect
35. #13090615C2×C3semidirect
36. D9×C9⋊C9C2×C3semidirect
37. D9×C9⋊C9C2×C3semidirect
67. #10624550C22×C3semidirect
68. C9×C9⋊C9C22×C3semidirect
69. C9×C9⋊C9C22×C3semidirect
153. D923−1+2semidirect
286. C9⋊D9C2×3−1+2semidirect
305. D9⋊C9AGL(1,ℤ/9)semidirect
306. D9⋊C9AGL(1,ℤ/9)semidirect
317. C9×D9C2×3−1+2semidirect
318. C9×D9C2×3−1+2semidirect
415. C9⋊C9C2×AGL(1,ℤ/9)semidirect
416. C9⋊C9C2×AGL(1,ℤ/9)semidirect
433. C92C22×3−1+2semidirect
680. D9#92264semidirect
681. D9#92264semidirect
727. C9C2×#92264semidirect
728. C9C2×#92264semidirect

Maximal subgroups

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

subgroupindex
#722435502
#722435252
#722433313
D9×D9⋊C93
D3×#922643
C3×#92265⋊C23