Finite Group Databasebeta

← #72220079

Subgroups — #72220079

Order 7776.

886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72220078—31nomaximal
2#72220077—31nomaximal
3#72220076C311yesmaximal, characteristic, complemented
4#72219995C211yesmaximal, characteristic, complemented
5#72219978C211yesmaximal, characteristic, complemented
6C2×#14517439C211yesmaximal, characteristic
7C23×#6900C2211yescharacteristic
8C22×#92265C411yescharacteristic, complemented
9C2×#11757618—21no—
10#14517439—21no—
11#14517439—21no—
12C2×#11757569—21no—
13C2×#11757569C411yescharacteristic, complemented
14C2×#67×3−1+2—31no—
15C2×C3×#611⋊C3D311yescharacteristic
16#13047994—31no—
17#13047994—31no—
18#13047994—61no—
193−1+2×#217—31no—
20C3×#3676⋊C3D311yescharacteristic
21C2×#611⋊C9—21no—
22C2×C9×#611C2×C311yescharacteristic
23#13046833C2×C311yescharacteristic, complemented
24#3676⋊C9—21no—
25C9×#3676C2×C311yescharacteristic, complemented
26C22×#6900—41no—
27C22×#6900C2×C411yescharacteristic
28C22×#6900D411yescharacteristic
29C22×#6900D411yescharacteristic
30C2×#92265—21no—
31C2×#92265—41no—
32#11757618—41no—
33#11757569—21no—
34#11757569—41no—
35C3×#63580—91no—
36#63393⋊C3—91no—
37#63365⋊C3—91no—
38#11720332—31no—
39#11720329—31no—
40C23×C3×3−1+2—21no—
41C23×C3×3−1+2C2×D311yescharacteristic
42C23×C3×3−1+2C2×D311yescharacteristic
43C22×D3×3−1+2—31no—
44C22×C3×AGL(1,ℤ/9)Dic311yescharacteristic
45C2×C3⋊(3−1+2⋊C4)—62no—
46C2×C3⋊(3−1+2⋊C4)—61no—
47C2×C3⋊(3−1+2⋊C4)—61no—
48#67×3−1+2—61no—
49#67×3−1+2—61no—
50C3×#611⋊C3—21no—
51C3×#611⋊C3—21no—
52C2×Dic3×3−1+2—31no—
53C2×Dic3×3−1+2—61no—
54C2×C3×3−1+2⋊C4—21no—
55C2×C3×3−1+2⋊C4Dic311yescharacteristic
56C23×C9⋊C9—21no—
57C23×C9⋊C9—21no—
58C23×C9⋊C9—41no—
59C23×C92C22×C311yescharacteristic
60C22×D9⋊C9—21no—
61C22×C9×D9C3×C411yescharacteristic, complemented
62C2×C9⋊Dic9—21no—
63#611⋊C9—22no—
64#611⋊C9—22no—
65C2×Dic9⋊C9—21no—
66C2×Dic9⋊C9—22no—
67C9×#611—21no—
68C9×#611—21no—
69C2×C9×Dic9—21no—
70C2×C9×Dic9C3×C411yescharacteristic, complemented
71C2×#6900—21no—
72C2×#6900—21no—
73C2×#6900—21no—
74C2×#6900C22⋊C411yescharacteristic
75#92265—41no—
76C2×C32×#67—31no—
77C3×#3757—91no—
78C32×#217—31no—
79C2×D4×3−1+2—91no—
80C2×#611⋊C3—31no—
81C2×C9×#67—31no—
82C2×C9×#67—61no—
83C2×C3×#611C3×D311yescharacteristic
84C22⋊C4×3−1+2—91no—
85#88551—31no—
86#88551—31no—
87#88551—61no—
88#3676⋊C3—31no—
89#3676⋊C3—91no—
90#3676⋊C3—91no—
91#3676⋊C3—181no—
92#3676⋊C3—181no—
93#3676⋊C3—183no—
94C9×#217—31no—
95C9×#217—61no—
96C3×#3676C3×D311yescharacteristic
97C22×C3×3−1+2—21no—
98C22×C3×3−1+2—21no—
99C22×C3×3−1+2—21no—
100C22×C3×3−1+2—41no—
101C22×C3×3−1+2—41no—
102C22×C3×3−1+2—42no—
103C22×C3×3−1+2C4×D311yescharacteristic
104C22×C3×3−1+2D1211yescharacteristic
105C22×C3×3−1+2C2×Dic311yescharacteristic
106C22×C3×3−1+2#6711yescharacteristic
107C22×C3×3−1+2#6711yescharacteristic
108C22×C3×3−1+2#6711yescharacteristic
109C2×D3×3−1+2—61no—
110C2×D3×3−1+2—121no—
111C2×C3×AGL(1,ℤ/9)—21no—
112C2×C3×AGL(1,ℤ/9)—41no—
113C3⋊(3−1+2⋊C4)—122no—
114C3⋊(3−1+2⋊C4)—121no—
115C3⋊(3−1+2⋊C4)—121no—
116Dic3×3−1+2—61no—
117Dic3×3−1+2—121no—
118C3×3−1+2⋊C4—21no—
119C3×3−1+2⋊C4—41no—
120C22×C9⋊C9—21no—
121C22×C9⋊C9—21no—
122C22×C9⋊C9—21no—
123C22×C9⋊C9—21no—
124C22×C9⋊C9—21no—
125C22×C9⋊C9—21no—
126C22×C9⋊C9—41no—
127C22×C9⋊C9—41no—
128C22×C9⋊C9—41no—
129C22×C9⋊C9—42no—
130C22×C9⋊C9—42no—
131C22×C9⋊C9—44no—
132C22×C92—41no—
133C22×C92C2×C3×C411yescharacteristic
134C22×C92C3×D411yescharacteristic
135C22×C92C3×D411yescharacteristic
136C2×D9⋊C9—22no—
137C2×D9⋊C9—42no—
138C2×C9×D9—21no—
139C2×C9×D9—41no—
140C9⋊Dic9—41no—
141Dic9⋊C9—22no—
142Dic9⋊C9—42no—
143C9×Dic9—21no—
144C9×Dic9—41no—
145C3×#834—271no—
146C3×#806—271no—
147#63580—91no—
148#63393—91no—
149#63365—91no—
150#6900#9911yescharacteristic, complemented, Sylow
151C23×C33D3211yescharacteristic
152C22×C32×D3—31no—
153C2×C3×C3⋊Dic3—181no—
154C32×#67—61no—
155C32×#67—61no—
156C2×C32×Dic3—31no—
157C2×C32×Dic3—61no—
158C23×3−1+2—31no—
159C23×3−1+2—31no—
160C23×3−1+2—61no—
161C23×3−1+2—61no—
162C23×3−1+2—63no—
163C23×3−1+2—91no—
164C23×C3×C9—21no—
165C23×C3×C9—21no—
166C23×C3×C9—21no—
167C23×C3×C9—41no—
168C23×C3×C9C2×C3×D311yescharacteristic
169C23×C3×C9C2×C3×D311yescharacteristic
170C22×AGL(1,ℤ/9)—31no—
171C22×D3×C9—31no—
172C22×D3×C9—61no—
173C22×C3×D9C3×Dic311yescharacteristic
174D4×3−1+2—181no—
175D4×3−1+2—181no—
176C2×C4×3−1+2—91no—
177C2×C4×3−1+2—181no—
178C2×C3⋊Dic9—62no—
179C2×C3⋊Dic9—61no—
180C2×C3⋊Dic9—61no—
181#611⋊C3—61no—
182#611⋊C3—61no—
183C2×3−1+2⋊C4—31no—
184C2×3−1+2⋊C4—61no—
185C2×3−1+2⋊C4—181no—
186C2×3−1+2⋊C4—181no—
187C2×3−1+2⋊C4—182no—
188C2×3−1+2⋊C4—182no—
189C2×3−1+2⋊C4—186no—
190C9×#67—62no—
191C9×#67—62no—
192C9×#67—61no—
193C9×#67—61no—
194C3×#611—21no—
195C3×#611—21no—
196C2×C9×Dic3—31no—
197C2×C9×Dic3—61no—
198C2×C9×Dic3—62no—
199C2×C9×Dic3—61no—
200C2×C3×Dic9—21no—
201C2×C3×Dic9C3×Dic311yescharacteristic
202C2×C3×3−1+2—21no—
203C2×C3×3−1+2—21no—
204C2×C3×3−1+2—22no—
205C2×C3×3−1+2—21no—
206C2×C3×3−1+2—21no—
207C2×C3×3−1+2—21no—
208C2×C3×3−1+2—21no—
209C2×C3×3−1+2—21no—
210C2×C3×3−1+2—41no—
211C2×C3×3−1+2—41no—
212C2×C3×3−1+2(C2×D3)⋊C411yescharacteristic
213C2×C3×3−1+2#21711yescharacteristic
214D3×3−1+2—121no—
215C3×AGL(1,ℤ/9)—41no—
216C2×C9⋊C9—22no—
217C2×C9⋊C9—22no—
218C2×C9⋊C9—21no—
219C2×C9⋊C9—21no—
220C2×C9⋊C9—41no—
221C2×C9⋊C9—41no—
222C2×C9⋊C9—41no—
223C2×C9⋊C9—41no—
224C2×C9⋊C9—41no—
225C2×C9⋊C9—42no—
226C2×C9⋊C9—42no—
227C2×C9⋊C9—42no—
228C2×C92—21no—
229C2×C92—21no—
230C2×C92—21no—
231C2×C92C3×C22⋊C411yescharacteristic
232D9⋊C9—42no—
233C9×D9—41no—
234C2×C32×D4—91no—
235C2×C3×#67—31no—
236C2×C3×#67—91no—
237C32×C22⋊C4—91no—
238#3757—91no—
239C3×#217—31no—
240C3×#217—91no—
241C3×#217—271no—
242C3×#217—271no—
243C3×#217—541no—
244C2×D4×C9—91no—
245C2×D4×C9—181no—
246C2×#611AGL(1,ℤ/9)11yescharacteristic
247C9×C22⋊C4—91no—
248C9×C22⋊C4—181no—
249#3676—91no—
250#3676—91no—
251#3676—181no—
252#3676—181no—
253#3676—183no—
254#3676AGL(1,ℤ/9)11yescharacteristic, complemented
255C22×C33—41no—
256C22×C33D3×Dic311yescharacteristic
257C22×C33#62511yescharacteristic
258C22×C33#62611yescharacteristic
259C2×C32×D3—61no—
260C2×C32×D3—121no—
261C3×C3⋊Dic3—361no—
262C32×Dic3—61no—
263C32×Dic3—121no—
264C22×3−1+2—31no—
265C22×3−1+2—31no—
266C22×3−1+2—31no—
267C22×3−1+2—31no—
268C22×3−1+2—31no—
269C22×3−1+2—31no—
270C22×3−1+2—61no—
271C22×3−1+2—61no—
272C22×3−1+2—63no—
273C22×3−1+2—61no—
274C22×3−1+2—61no—
275C22×3−1+2—61no—
276C22×3−1+2—61no—
277C22×3−1+2—63no—
278C22×3−1+2—63no—
279C22×3−1+2—121no—
280C22×3−1+2—121no—
281C22×3−1+2—122no—
282C22×3−1+2—122no—
283C22×3−1+2—126no—
284C22×3−1+2—181no—
285C22×3−1+2—361no—
286C22×C3×C9—21no—
287C22×C3×C9—21no—
288C22×C3×C9—21no—
289C22×C3×C9—21no—
290C22×C3×C9—21no—
291C22×C3×C9—21no—
292C22×C3×C9—21no—
293C22×C3×C9—21no—
294C22×C3×C9—21no—
295C22×C3×C9—41no—
296C22×C3×C9—41no—
297C22×C3×C9—42no—
298C22×C3×C9—42no—
299C22×C3×C9—42no—
300C22×C3×C9—44no—
301C22×C3×C9—41no—
302C22×C3×C9—41no—
303C22×C3×C9—41no—
304C22×C3×C9C3×C4×D311yescharacteristic
305C22×C3×C9C3×D1211yescharacteristic
306C22×C3×C9C2×C3×Dic311yescharacteristic
307C22×C3×C9C3×#6711yescharacteristic
308C22×C3×C9C3×#6711yescharacteristic
309C22×C3×C9C3×#6711yescharacteristic
310C2×AGL(1,ℤ/9)—61no—
311C2×AGL(1,ℤ/9)—121no—
312C2×D3×C9—62no—
313C2×D3×C9—61no—
314C2×D3×C9—122no—
315C2×D3×C9—121no—
316C2×C3×D9—21no—
317C2×C3×D9—41no—
318C4×3−1+2—181no—
319C4×3−1+2—361no—
320C3⋊Dic9—122no—
321C3⋊Dic9—121no—
322C3⋊Dic9—121no—
3233−1+2⋊C4—61no—
3243−1+2⋊C4—121no—
3253−1+2⋊C4—361no—
3263−1+2⋊C4—361no—
3273−1+2⋊C4—362no—
3283−1+2⋊C4—362no—
3293−1+2⋊C4—366no—
330C9×Dic3—62no—
331C9×Dic3—61no—
332C9×Dic3—121no—
333C9×Dic3—122no—
334C3×Dic9—21no—
335C3×Dic9—41no—
336C3×#99—811no—
337#834—271no—
338#806—271no—
339C3×3−1+2—21no—
340C3×3−1+2#80611yescharacteristic
341C3×3−1+2#83411yescharacteristic
342C9⋊C9—21no—
343C9⋊C9—21no—
344C9⋊C9—41no—
345C92C3×#9911yescharacteristic, complemented
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—61no—
349C23×C32—91no—
350C23×C32C3×D3211yescharacteristic
351C22×C3×D3—31no—
352C22×C3×D3—91no—
353C32×D4—181no—
354C32×D4—181no—
355C2×C32×C4—91no—
356C2×C32×C4—181no—
357C2×C3⋊Dic3—181no—
358C3×#67—61no—
359C3×#67—61no—
360C3×#67—181no—
361C3×#67—181no—
362C2×C3×Dic3—31no—
363C2×C3×Dic3—61no—
364C2×C3×Dic3—91no—
365C2×C3×Dic3—181no—
366C2×C3×Dic3—541no—
367C2×C3×Dic3—541no—
368C2×C3×Dic3—542no—
369C23×C9—23no—
370C23×C9—21no—
371C23×C9—21no—
372C23×C9—61no—
373C23×C9—61no—
374C23×C9—91no—
375C23×C9—121no—
376C23×C9—181no—
377C23×C9C2×AGL(1,ℤ/9)11yescharacteristic
378C23×C9C2×AGL(1,ℤ/9)11yescharacteristic
379C22×D93−1+2⋊C411yescharacteristic, complemented
380D4×C9—182no—
381D4×C9—182no—
382D4×C9—181no—
383D4×C9—181no—
384C2×C4×C9—91no—
385C2×C4×C9—181no—
386C2×C4×C9—182no—
387C2×C4×C9—181no—
388#611—21no—
389#611—21no—
390C2×Dic9—21no—
391C2×Dic9—186no—
392C2×Dic9—182no—
393C2×Dic9—182no—
394C2×Dic9—181no—
395C2×Dic9—181no—
396C2×Dic93−1+2⋊C411yescharacteristic, complemented
397C2×C33—21no—
398C2×C33—21no—
399C2×C33—21no—
400C2×C33(C2×D3)⋊Dic311yescharacteristic
401C32×D3—121no—
402C2×3−1+2—31no—
403C2×3−1+2—31no—
404C2×3−1+2—61no—
405C2×3−1+2—61no—
406C2×3−1+2—61no—
407C2×3−1+2—61no—
408C2×3−1+2—61no—
409C2×3−1+2—61no—
410C2×3−1+2—61no—
411C2×3−1+2—61no—
412C2×3−1+2—62no—
413C2×3−1+2—62no—
414C2×3−1+2—66no—
415C2×3−1+2—63no—
416C2×3−1+2—121no—
417C2×3−1+2—121no—
418C2×3−1+2—123no—
419C2×3−1+2—123no—
420C2×3−1+2—121no—
421C2×3−1+2—121no—
422C2×3−1+2—361no—
423C2×C3×C9—22no—
424C2×C3×C9—21no—
425C2×C3×C9—21no—
426C2×C3×C9—21no—
427C2×C3×C9—21no—
428C2×C3×C9—21no—
429C2×C3×C9—21no—
430C2×C3×C9—21no—
431C2×C3×C9—22no—
432C2×C3×C9—22no—
433C2×C3×C9—21no—
434C2×C3×C9—21no—
435C2×C3×C9—41no—
436C2×C3×C9—41no—
437C2×C3×C9—41no—
438C2×C3×C9—41no—
439C2×C3×C9—41no—
440C2×C3×C9—41no—
441C2×C3×C9—42no—
442C2×C3×C9—42no—
443C2×C3×C9—42no—
444C2×C3×C9—41no—
445C2×C3×C9C3×(C2×D3)⋊C411yescharacteristic
446C2×C3×C9C3×#21711yescharacteristic
447AGL(1,ℤ/9)—121no—
448D3×C9—122no—
449D3×C9—121no—
450C3×D9—41no—
451C2×C3×D4—91no—
452C2×C3×D4—271no—
453C2×#67—31no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4—271no—
456C3×C22⋊C4—811no—
457#217—31no—
458#217—271no—
459#217—271no—
460#217—541no—
461C22×C32—31no—
462C22×C32—31no—
463C22×C32—31no—
464C22×C32—31no—
465C22×C32—31no—
466C22×C32—31no—
467C22×C32—41no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—121no—
472C22×C32—121no—
473C22×C32—122no—
474C22×C32—181no—
475C22×C32—361no—
476C22×C32C3×D3×Dic311yescharacteristic
477C22×C32C3×#62511yescharacteristic
478C22×C32C3×#62611yescharacteristic
479C2×C3×D3—61no—
480C2×C3×D3—121no—
481C2×C3×D3—181no—
482C2×C3×D3—361no—
483C32×C4—181no—
484C32×C4—361no—
485C3⋊Dic3—361no—
486C3×Dic3—61no—
487C3×Dic3—121no—
488C3×Dic3—181no—
489C3×Dic3—361no—
490C3×Dic3—1081no—
491C3×Dic3—1081no—
492C3×Dic3—1082no—
493C22×C9—23no—
494C22×C9—23no—
495C22×C9—23no—
496C22×C9—21no—
497C22×C9—21no—
498C22×C9—21no—
499C22×C9—21no—
500C22×C9—21no—
501C22×C9—21no—
502C22×C9—41no—
503C22×C9—41no—
504C22×C9—42no—
505C22×C9—42no—
506C22×C9—46no—
507C22×C9—61no—
508C22×C9—61no—
509C22×C9—61no—
510C22×C9—61no—
511C22×C9—61no—
512C22×C9—61no—
513C22×C9—121no—
514C22×C9—121no—
515C22×C9—121no—
516C22×C9—122no—
517C22×C9—122no—
518C22×C9—124no—
519C22×C9—182no—
520C22×C9—181no—
521C22×C9—361no—
522C22×C9—362no—
523C22×C9C4×AGL(1,ℤ/9)11yescharacteristic
524C22×C9C4⋊AGL(1,ℤ/9)11yescharacteristic
525C22×C9C2×3−1+2⋊C411yescharacteristic
526C22×C9#611⋊C311yescharacteristic
527C22×C9#611⋊C311yescharacteristic
528C22×C9#611⋊C311yescharacteristic
529C2×D9—21no—
530C2×D9—41no—
531C4×C9—182no—
532C4×C9—181no—
533C4×C9—361no—
534C4×C9—362no—
535Dic9—21no—
536Dic9—41no—
537Dic9—366no—
538Dic9—362no—
539Dic9—362no—
540Dic9—361no—
541Dic9—361no—
542#99—811noSylow
543C33#6358011yescharacteristic
5443−1+2—31no—
5453−1+2—31no—
5463−1+2—61no—
5473−1+2—61no—
5483−1+2—63no—
549C3×C9—21no—
550C3×C9—21no—
551C3×C9—21no—
552C3×C9—41no—
553C3×C9C3×#80611yescharacteristic
554C3×C9C3×#83411yescharacteristic
555C23×C3—21no—
556C23×C3—91no—
557C23×C3—91no—
558C23×C3—271no—
559C23×C3D3×AGL(1,ℤ/9)11yescharacteristic
560C23×C3D3×AGL(1,ℤ/9)11yescharacteristic
561C22×D3—31no—
562C3×D4—181no—
563C3×D4—181no—
564C3×D4—541no—
565C3×D4—541no—
566C2×C3×C4—91no—
567C2×C3×C4—181no—
568C2×C3×C4—271no—
569C2×C3×C4—541no—
570C2×C3×C4—1621no—
571#67—61no—
572#67—61no—
573C2×Dic3—31no—
574C2×Dic3—61no—
575C2×Dic3—542no—
576C2×Dic3—541no—
577C2×Dic3—541no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—31no—
582C2×C32—31no—
583C2×C32—61no—
584C2×C32—61no—
585C2×C32—61no—
586C2×C32—61no—
587C2×C32—61no—
588C2×C32—61no—
589C2×C32—61no—
590C2×C32—62no—
591C2×C32—121no—
592C2×C32—121no—
593C2×C32—361no—
594C2×C32C3×(C2×D3)⋊Dic311yescharacteristic
595C3×D3—121no—
596C3×D3—361no—
597C2×C9—26no—
598C2×C9—22no—
599C2×C9—22no—
600C2×C9—23no—
601C2×C9—21no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—21no—
605C2×C9—21no—
606C2×C9—21no—
607C2×C9—21no—
608C2×C9—21no—
609C2×C9—41no—
610C2×C9—41no—
611C2×C9—41no—
612C2×C9—41no—
613C2×C9—43no—
614C2×C9—43no—
615C2×C9—62no—
616C2×C9—62no—
617C2×C9—61no—
618C2×C9—61no—
619C2×C9—121no—
620C2×C9—121no—
621C2×C9—121no—
622C2×C9—121no—
623C2×C9—122no—
624C2×C9—121no—
625C2×C9—122no—
626C2×C9—122no—
627C2×C9—362no—
628C2×C9—361no—
629C2×C9(C2×AGL(1,ℤ/9))⋊C411yescharacteristic
630C2×C9#3676⋊C311yescharacteristic
631D9—41no—
632C2×D4—91no—
633C22⋊C4—91no—
634C22⋊C4—811no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—42no—
641C22×C3—91no—
642C22×C3—91no—
643C22×C3—91no—
644C22×C3—181no—
645C22×C3—361no—
646C22×C3—361no—
647C22×C3—541no—
648C22×C3—1081no—
649C22×C3Dic3×AGL(1,ℤ/9)11yescharacteristic
650C22×C3#6192⋊C311yescharacteristic
651C22×C3D3×3−1+2⋊C411yescharacteristic
652C22×C3#6194⋊C311yescharacteristic
653C22×C3#6194⋊C311yescharacteristic
654C22×C3#6195⋊C311yescharacteristic
655C2×D3—61no—
656C2×D3—121no—
657C3×C4—181no—
658C3×C4—361no—
659C3×C4—541no—
660C3×C4—3241no—
661C3×C4—1081no—
662Dic3—61no—
663Dic3—121no—
664Dic3—1082no—
665Dic3—1081no—
666Dic3—1081no—
667C32—31no—
668C32—31no—
669C32—61no—
670C32C3×#6358011yescharacteristic
671C9—23no—
672C9—21no—
673C9—21no—
674C9—61no—
675C9—61no—
676C9—121no—
677C9#63365⋊C311yescharacteristic, complemented
678C9#63393⋊C311yescharacteristic, complemented
679C23—91no—
680C23#92265⋊C211yescharacteristic
681D4—181no—
682D4—181no—
683C2×C4—91no—
684C2×C4—181no—
685C2×C4—1621no—
686C2×C3—22no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—91no—
697C2×C3—181no—
698C2×C3—181no—
699C2×C3—181no—
700C2×C3—361no—
701C2×C3—1081no—
702C2×C3(C2×AGL(1,ℤ/9))⋊Dic311yescharacteristic
703C2×C3(C2×D3)⋊(3−1+2⋊C4)11yescharacteristic
704D3—121no—
705C22—41no—
706C22—181no—
707C22—361no—
708C22#92265⋊C411yescharacteristic
709C22#1451682811yescharacteristic
710C22#1451682911yescharacteristic
711C4—181no—
712C4—361no—
713C4—3241no—
714C3—21no—
715C3—91no—
716C3#7222007711yescharacteristic
717C3#7222007811yescharacteristic
718C2—21no—
719C2—21no—
720C2—21no—
721C2—361no—
722C2#7221996911yescharacteristic
subgroupG/H
centerC2#72219969
commutatorC22×C92C2×C3×C4
FrattiniC23×C32C3×D32
FittingC23×#6900C22
socleC2×C32C3×(C2×D3)⋊Dic3
prime radicalC2×C3×#611⋊C3D3
cosocleC23×C92C22×C3
hypercenterC23#92265⋊C2
hypocenterC92C3×#99
LCSG ▷ C22×C92 ▷ C2×C92 ▷ C92
UCSC1 ◁ C2 ◁ C23

Complements

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

NH ≅ G/Ntype
3. #72220076C3semidirect
4. #72219995C2semidirect
5. #72219978C2semidirect
8. C22×#92265C4semidirect
13. C2×#11757569C4semidirect
23. #13046833C2×C3semidirect
25. C9×#3676C2×C3semidirect
61. C22×C9×D9C3×C4semidirect
70. C2×C9×Dic9C3×C4semidirect
150. #6900#99semidirect
254. #3676AGL(1,ℤ/9)semidirect
345. C92C3×#99semidirect
379. C22×D93−1+2⋊C4semidirect
396. C2×Dic93−1+2⋊C4semidirect
677. C9#63365⋊C3semidirect
678. C9#63393⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722200783
#722200773
#722200763
#722199952
#722199782
C2×#145174392