Finite Group Databasebeta

← #72220035

Subgroups — #72220035

Order 7776.

1848 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72220033—31nomaximal
2#72220031—31nomaximal
3#72220029C311yesmaximal, characteristic, complemented
4#72219978C211yesmaximal, characteristic, complemented
5#72219969C212yesmaximal, complemented
6C23×#92265C211yesmaximal, characteristic, complemented
7C2×#14516829C212yesmaximal, complemented
8C2×#14517678C211yesmaximal, characteristic, complemented
9C23×#6900C2211yescharacteristic
10C22×#92314C2211yescharacteristic, complemented
11C22×#92265—22no—
12C22×#92265—24no—
13C22×#92265C2212yes—
14#14517678—22no—
15C2×#11757618C2211yescharacteristic, complemented
16C2×#11757569C2212yescomplemented
17#14516829—24no—
18C23×D3×3−1+2—31no—
19C23×C3×AGL(1,ℤ/9)D311yescharacteristic
20C2×#10619980—31no—
21C2×#10619980—31no—
22C2×#10619980—61no—
23C2×#6195⋊C3—32no—
24C2×#6192⋊C3—32no—
25C23×D9⋊C9—21no—
26C23×C9×D9C2×C311yescharacteristic, complemented
273−1+2×#217—31no—
28C3×#3676⋊C3D311yescharacteristic
29(C2×D3)⋊(3−1+2⋊C4)—32no—
30(C2×AGL(1,ℤ/9))⋊Dic3—32no—
31C2×#10619673C2×C311yescharacteristic, complemented
32C2×#10619530C2×C312yescomplemented
33#3676⋊C9—21no—
34C9×#3676C2×C311yescharacteristic, complemented
35(C2×D9)⋊Dic9C2×C312yescomplemented
36C22×#6900—22no—
37C22×#6900D412yescomplemented
38C22×#6900C2311yescharacteristic
39C2×#92314—21no—
40C2×#92314—22no—
41C2×#92265—28no—
42C2×#92265—22no—
43C2×#92265—22no—
44C2×#92265D414yescomplemented
45#11757618—21no—
46#11757569—22no—
47C3×#63977—91no—
48#11721704—91no—
49#63444⋊C3—91no—
50#11721287—31no—
51#11721276—31no—
52C23×C3×3−1+2—21no—
53C23×C3×3−1+2C2×D311yescharacteristic
54C23×C3×3−1+2C2×D311yescharacteristic
55C22×C3⋊AGL(1,ℤ/9)—31no—
56C22×C3⋊AGL(1,ℤ/9)—31no—
57C22×C3⋊AGL(1,ℤ/9)—61no—
58C22×D3×3−1+2—32no—
59C22×D3×3−1+2—64no—
60C22×D3×3−1+2—62no—
61C22×C3×AGL(1,ℤ/9)—22no—
62C22×C3×AGL(1,ℤ/9)—24no—
63C22×C3×AGL(1,ℤ/9)C2×D312yes—
64#10619980—64no—
65#10619980—62no—
66#10619980—62no—
67C2×C3⋊(3−1+2⋊C4)—31no—
68C2×C3⋊(3−1+2⋊C4)—31no—
69C2×C3⋊(3−1+2⋊C4)—61no—
70C2×Dic3×3−1+2—32no—
71C2×C3×3−1+2⋊C4C2×D312yes—
72#6195⋊C3—64no—
73#6192⋊C3—64no—
74C23×C9⋊C9—21no—
75C23×C9⋊C9—21no—
76C23×C9⋊C9—41no—
77C23×C92C22×C311yescharacteristic
78C22×C9⋊D9C22×C311yescharacteristic, complemented
79C22×D9⋊C9—24no—
80C22×D9⋊C9—28no—
81C22×D9⋊C9—22no—
82C22×C9×D9—22no—
83C22×C9×D9—24no—
84C22×C9×D9C22×C312yes—
85#10619673—22no—
86C2×C9⋊Dic9C22×C311yescharacteristic, complemented
87C2×Dic9⋊C9—22no—
88C2×C9×Dic9C22×C312yescomplemented
89#10619530—24no—
90C2×#6900—22no—
91C2×#6900C2×D411yescharacteristic
92C2×#6900C2×D412yes—
93#92314—41no—
94#92265—24no—
95C23×C32×D3—31no—
96C2×C3×#638—91no—
97C2×C3×#626—92no—
98C24×3−1+2—91no—
99C23×AGL(1,ℤ/9)—31no—
100C23×D3×C9—31no—
101C23×D3×C9—61no—
102C23×C3×D9C3×D311yescharacteristic
103C32×#217—31no—
104C3×(C2×D3)⋊Dic3—92no—
105C2×#6233—31no—
106C2×#6233—31no—
107C2×#6233—61no—
108C2×#611⋊C3—92no—
109C2×#611⋊C3—91no—
110C2×#611⋊C3—91no—
111C2×#611⋊C3—181no—
112C2×#611⋊C3—181no—
113C2×#611⋊C3—183no—
114C2×C4⋊AGL(1,ℤ/9)—92no—
115C2×#6195—32no—
116C2×#6192—32no—
117C22⋊C4×3−1+2—91no—
118#3676⋊C3—31no—
119#3676⋊C3—92no—
120C9×#217—31no—
121C9×#217—61no—
122C3×#3676C3×D311yescharacteristic
123(C2×AGL(1,ℤ/9))⋊C4—92no—
124(C2×D3)⋊Dic9—32no—
125(C2×D9)⋊Dic3—32no—
126C22×C3×3−1+2—22no—
127C22×C3×3−1+2—22no—
128C22×C3×3−1+2—21no—
129C22×C3×3−1+2—22no—
130C22×C3×3−1+2—42no—
131C22×C3×3−1+2D1212yes—
132C22×C3×3−1+2#6712yes—
133C22×C3×3−1+2C22×D311yescharacteristic
134C22×C3×3−1+2C22×D311yescharacteristic
135C2×C3⋊AGL(1,ℤ/9)—62no—
136C2×C3⋊AGL(1,ℤ/9)—61no—
137C2×C3⋊AGL(1,ℤ/9)—61no—
138C2×C3⋊AGL(1,ℤ/9)—62no—
139C2×C3⋊AGL(1,ℤ/9)—62no—
140C2×C3⋊AGL(1,ℤ/9)—122no—
141C2×D3×3−1+2—34no—
142C2×D3×3−1+2—68no—
143C2×D3×3−1+2—62no—
144C2×D3×3−1+2—62no—
145C2×C3×AGL(1,ℤ/9)—28no—
146C2×C3×AGL(1,ℤ/9)—22no—
147C2×C3×AGL(1,ℤ/9)—22no—
148C2×C3×AGL(1,ℤ/9)#6714yes—
149C3⋊(3−1+2⋊C4)—62no—
150C3⋊(3−1+2⋊C4)—61no—
151C3⋊(3−1+2⋊C4)—61no—
152Dic3×3−1+2—62no—
153C3×3−1+2⋊C4—22no—
154C22×C9⋊C9—24no—
155C22×C9⋊C9—22no—
156C22×C9⋊C9—22no—
157C22×C9⋊C9—21no—
158C22×C9⋊C9—21no—
159C22×C9⋊C9—42no—
160C22×C9⋊C9—41no—
161C22×C9⋊C9—42no—
162C22×C9⋊C9—44no—
163C22×C92—22no—
164C22×C92C3×D412yescomplemented
165C22×C92C23×C311yescharacteristic
166C2×C9⋊D9—21no—
167C2×C9⋊D9—22no—
168C2×D9⋊C9—216no—
169C2×D9⋊C9—24no—
170C2×D9⋊C9—24no—
171C2×D9⋊C9—24no—
172C2×C9×D9—28no—
173C2×C9×D9—22no—
174C2×C9×D9—22no—
175C2×C9×D9C3×D414yescomplemented
176C9⋊Dic9—21no—
177Dic9⋊C9—42no—
178C9×Dic9—22no—
179C3×#953—271no—
180C3×#882—271no—
181#63977—91no—
182#63515—91no—
183#63444—91no—
184#6900#12011yescharacteristic, complemented, Sylow
185C23×C33D3211yescharacteristic
186C22×C3×C3⋊D3—91no—
187C22×C32×D3—32no—
188C22×C32×D3—64no—
189C22×C32×D3—62no—
190C3×#638—182no—
191C2×C3×C3⋊Dic3—91no—
192C2×C32×Dic3—32no—
193C3×#626—184no—
194C23×3−1+2—31no—
195C23×3−1+2—31no—
196C23×3−1+2—61no—
197C23×3−1+2—61no—
198C23×3−1+2—63no—
199C23×3−1+2—92no—
200C23×3−1+2—182no—
201C23×3−1+2—184no—
202C23×C3×C9—21no—
203C23×C3×C9—21no—
204C23×C3×C9—21no—
205C23×C3×C9—41no—
206C23×C3×C9C2×C3×D311yescharacteristic
207C23×C3×C9C2×C3×D311yescharacteristic
208C22×C3⋊D9—31no—
209C22×C3⋊D9—31no—
210C22×C3⋊D9—61no—
211C22×AGL(1,ℤ/9)—32no—
212C22×AGL(1,ℤ/9)—64no—
213C22×AGL(1,ℤ/9)—62no—
214C22×AGL(1,ℤ/9)—91no—
215C22×AGL(1,ℤ/9)—91no—
216C22×AGL(1,ℤ/9)—181no—
217C22×AGL(1,ℤ/9)—181no—
218C22×AGL(1,ℤ/9)—183no—
219C22×D3×C9—32no—
220C22×D3×C9—64no—
221C22×D3×C9—62no—
222C22×D3×C9—68no—
223C22×D3×C9—64no—
224C22×D3×C9—62no—
225C22×C3×D9—22no—
226C22×C3×D9—24no—
227C22×C3×D9C2×C3×D312yes—
228C2×C4×3−1+2—92no—
229#6233—64no—
230#6233—62no—
231#6233—62no—
232C2×C3⋊Dic9—31no—
233C2×C3⋊Dic9—31no—
234C2×C3⋊Dic9—61no—
235#611⋊C3—184no—
236#611⋊C3—182no—
237#611⋊C3—182no—
238#611⋊C3—184no—
239#611⋊C3—184no—
240#611⋊C3—1812no—
241C2×3−1+2⋊C4—32no—
242C2×3−1+2⋊C4—91no—
243C2×3−1+2⋊C4—91no—
244C2×3−1+2⋊C4—181no—
245C2×3−1+2⋊C4—181no—
246C2×3−1+2⋊C4—183no—
247C2×C9×Dic3—32no—
248C2×C9×Dic3—62no—
249C2×C3×Dic9C2×C3×D312yes—
250C4⋊AGL(1,ℤ/9)—184no—
251#6195—64no—
252#6192—64no—
253C2×C3×3−1+2—22no—
254C2×C3×3−1+2—21no—
255C2×C3×3−1+2—22no—
256C2×C3×3−1+2—22no—
257C2×C3×3−1+2—42no—
258C2×C3×3−1+2C2×D1211yescharacteristic
259C2×C3×3−1+2D3×D412yes—
260C2×C3×3−1+2C2×#6711yescharacteristic
261C2×C3×3−1+2C2×#6712yes—
262C3⋊AGL(1,ℤ/9)—122no—
263C3⋊AGL(1,ℤ/9)—121no—
264C3⋊AGL(1,ℤ/9)—121no—
265D3×3−1+2—64no—
266C3×AGL(1,ℤ/9)—24no—
267C2×C9⋊C9—24no—
268C2×C9⋊C9—21no—
269C2×C9⋊C9—22no—
270C2×C9⋊C9—21no—
271C2×C9⋊C9—22no—
272C2×C9⋊C9—41no—
273C2×C9⋊C9—42no—
274C2×C9⋊C9—42no—
275C2×C9⋊C9—44no—
276C2×C92—22no—
277C2×C92C2×C3×D411yescharacteristic
278C2×C92C2×C3×D412yes—
279C9⋊D9—41no—
280D9⋊C9—28no—
281C9×D9—24no—
282C24×C32—91no—
283C23×C3×D3—31no—
284C23×C3×D3—91no—
285C2×#638—91no—
286C2×C3×#67—272no—
287C2×C3×#67—271no—
288C2×C3×#67—271no—
289C2×C3×#67—541no—
290C2×C3×D12—272no—
291C2×#626—92no—
292C24×C9—91no—
293C24×C9—181no—
294C23×D9AGL(1,ℤ/9)11yescharacteristic, complemented
295C32×C22⋊C4—91no—
296C3×#217—31no—
297C3×#217—91no—
298C3×#217—272no—
299C3×(C2×D3)⋊C4—272no—
300(C2×D3)⋊Dic3—92no—
301C2×#611—91no—
302C2×#611—91no—
303C2×#611—92no—
304C2×#611—181no—
305C2×#611—181no—
306C2×#611—183no—
307C2×D36—92no—
308C9×C22⋊C4—91no—
309C9×C22⋊C4—181no—
310#3676—92no—
311#3676AGL(1,ℤ/9)11yescharacteristic, complemented
312(C2×D9)⋊C4—92no—
313C22×C33—22no—
314C22×C33#62612yes—
315C22×C33C2×D3211yescharacteristic
316C2×C3×C3⋊D3—181no—
317C2×C3×C3⋊D3—182no—
318C2×C32×D3—34no—
319C2×C32×D3—68no—
320C2×C32×D3—62no—
321C2×C32×D3—62no—
322C3×C3⋊Dic3—181no—
323C32×Dic3—62no—
324C22×3−1+2—31no—
325C22×3−1+2—31no—
326C22×3−1+2—32no—
327C22×3−1+2—32no—
328C22×3−1+2—62no—
329C22×3−1+2—62no—
330C22×3−1+2—61no—
331C22×3−1+2—61no—
332C22×3−1+2—63no—
333C22×3−1+2—62no—
334C22×3−1+2—62no—
335C22×3−1+2—66no—
336C22×3−1+2—94no—
337C22×3−1+2—122no—
338C22×3−1+2—126no—
339C22×3−1+2—122no—
340C22×3−1+2—182no—
341C22×3−1+2—182no—
342C22×3−1+2—188no—
343C22×C3×C9—21no—
344C22×C3×C9—24no—
345C22×C3×C9—22no—
346C22×C3×C9—21no—
347C22×C3×C9—21no—
348C22×C3×C9—22no—
349C22×C3×C9—22no—
350C22×C3×C9—22no—
351C22×C3×C9—22no—
352C22×C3×C9—42no—
353C22×C3×C9—42no—
354C22×C3×C9—44no—
355C22×C3×C9—42no—
356C22×C3×C9—41no—
357C22×C3×C9C3×D1212yes—
358C22×C3×C9C3×#6712yes—
359C22×C3×C9C22×C3×D311yescharacteristic
360C22×C3×C9C22×C3×D311yescharacteristic
361C2×C3⋊D9—62no—
362C2×C3⋊D9—61no—
363C2×C3⋊D9—62no—
364C2×C3⋊D9—61no—
365C2×C3⋊D9—62no—
366C2×C3⋊D9—122no—
367C2×AGL(1,ℤ/9)—34no—
368C2×AGL(1,ℤ/9)—62no—
369C2×AGL(1,ℤ/9)—62no—
370C2×AGL(1,ℤ/9)—68no—
371C2×AGL(1,ℤ/9)—182no—
372C2×AGL(1,ℤ/9)—181no—
373C2×AGL(1,ℤ/9)—182no—
374C2×AGL(1,ℤ/9)—181no—
375C2×AGL(1,ℤ/9)—182no—
376C2×AGL(1,ℤ/9)—182no—
377C2×AGL(1,ℤ/9)—186no—
378C2×AGL(1,ℤ/9)—362no—
379C2×AGL(1,ℤ/9)—362no—
380C2×AGL(1,ℤ/9)—366no—
381C2×D3×C9—34no—
382C2×D3×C9—64no—
383C2×D3×C9—68no—
384C2×D3×C9—616no—
385C2×D3×C9—64no—
386C2×D3×C9—64no—
387C2×D3×C9—62no—
388C2×D3×C9—62no—
389C2×C3×D9—28no—
390C2×C3×D9—22no—
391C2×C3×D9—22no—
392C2×C3×D9C3×#6714yes—
393C4×3−1+2—182no—
394C3⋊Dic9—62no—
395C3⋊Dic9—61no—
396C3⋊Dic9—61no—
3973−1+2⋊C4—62no—
3983−1+2⋊C4—181no—
3993−1+2⋊C4—181no—
4003−1+2⋊C4—182no—
4013−1+2⋊C4—182no—
4023−1+2⋊C4—186no—
403C9×Dic3—62no—
404C9×Dic3—122no—
405C3×Dic9—22no—
406C3×#120—811no—
407#953—271no—
408#882—271no—
409C3×3−1+2—21no—
410C3×3−1+2#88211yescharacteristic
411C3×3−1+2#95311yescharacteristic
412C9⋊C9—21no—
413C9⋊C9—21no—
414C9⋊C9—41no—
415C92C3×#12011yescharacteristic, complemented
416C23×C32—31no—
417C23×C32—31no—
418C23×C32—61no—
419C23×C32—92no—
420C23×C32—182no—
421C23×C32—184no—
422C23×C32C3×D3211yescharacteristic
423C22×C3⋊D3—91no—
424C22×C3×D3—32no—
425C22×C3×D3—64no—
426C22×C3×D3—62no—
427C22×C3×D3—92no—
428C22×C3×D3—184no—
429C22×C3×D3—182no—
430C22×C3×D3—271no—
431C22×C3×D3—271no—
432C22×C3×D3—541no—
433C2×C32×C4—92no—
434#638—182no—
435C2×C3⋊Dic3—91no—
436C3×#67—544no—
437C3×#67—542no—
438C3×#67—542no—
439C3×#67—544no—
440C2×C3×Dic3—32no—
441C2×C3×Dic3—92no—
442C2×C3×Dic3—271no—
443C2×C3×Dic3—271no—
444C2×C3×Dic3—541no—
445C3×D12—544no—
446#626—184no—
447C23×C9—23no—
448C23×C9—21no—
449C23×C9—21no—
450C23×C9—61no—
451C23×C9—61no—
452C23×C9—92no—
453C23×C9—121no—
454C23×C9—182no—
455C23×C9—184no—
456C23×C9—188no—
457C23×C9—184no—
458C23×C9—182no—
459C23×C9C2×AGL(1,ℤ/9)11yescharacteristic
460C23×C9C2×AGL(1,ℤ/9)11yescharacteristic
461C22×D9—22no—
462C22×D9—24no—
463C22×D9—91no—
464C22×D9—91no—
465C22×D9—181no—
466C22×D9—181no—
467C22×D9—183no—
468C22×D9C2×AGL(1,ℤ/9)12yes—
469C2×C4×C9—92no—
470C2×C4×C9—182no—
471#611—184no—
472#611—1812no—
473#611—184no—
474#611—184no—
475#611—182no—
476#611—182no—
477C2×Dic9—91no—
478C2×Dic9—91no—
479C2×Dic9—181no—
480C2×Dic9—181no—
481C2×Dic9—183no—
482C2×Dic9C2×AGL(1,ℤ/9)12yescomplemented
483D36—184no—
484C2×C33—22no—
485C2×C33C2×#62611yescharacteristic
486C2×C33D3×#6712yes—
487C3×C3⋊D3—361no—
488C32×D3—64no—
489C2×3−1+2—31no—
490C2×3−1+2—32no—
491C2×3−1+2—31no—
492C2×3−1+2—32no—
493C2×3−1+2—62no—
494C2×3−1+2—61no—
495C2×3−1+2—61no—
496C2×3−1+2—62no—
497C2×3−1+2—62no—
498C2×3−1+2—62no—
499C2×3−1+2—63no—
500C2×3−1+2—66no—
501C2×3−1+2—122no—
502C2×3−1+2—126no—
503C2×3−1+2—122no—
504C2×3−1+2—184no—
505C2×C3×C9—21no—
506C2×C3×C9—22no—
507C2×C3×C9—22no—
508C2×C3×C9—22no—
509C2×C3×C9—24no—
510C2×C3×C9—21no—
511C2×C3×C9—21no—
512C2×C3×C9—22no—
513C2×C3×C9—22no—
514C2×C3×C9—42no—
515C2×C3×C9—42no—
516C2×C3×C9—44no—
517C2×C3×C9—41no—
518C2×C3×C9—42no—
519C2×C3×C9C2×C3×D1211yescharacteristic
520C2×C3×C9C3×D3×D412yes—
521C2×C3×C9C2×C3×#6711yescharacteristic
522C2×C3×C9C2×C3×#6712yes—
523C3⋊D9—122no—
524C3⋊D9—121no—
525C3⋊D9—121no—
526AGL(1,ℤ/9)—64no—
527AGL(1,ℤ/9)—361no—
528AGL(1,ℤ/9)—361no—
529AGL(1,ℤ/9)—362no—
530AGL(1,ℤ/9)—362no—
531AGL(1,ℤ/9)—366no—
532D3×C9—68no—
533D3×C9—64no—
534C3×D9—24no—
535C24×C3—91no—
536C24×C3—271no—
537C23×D3—31no—
538C2×C3×D4—812no—
539C2×C3×D4—811no—
540C2×#67—272no—
541C2×#67—271no—
542C2×#67—271no—
543C2×#67—541no—
544C2×D12—272no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—271no—
547C3×C22⋊C4—812no—
548#217—31no—
549#217—272no—
550(C2×D3)⋊C4—272no—
551C22×C32—22no—
552C22×C32—31no—
553C22×C32—31no—
554C22×C32—32no—
555C22×C32—32no—
556C22×C32—61no—
557C22×C32—62no—
558C22×C32—62no—
559C22×C32—62no—
560C22×C32—94no—
561C22×C32—122no—
562C22×C32—182no—
563C22×C32—182no—
564C22×C32—188no—
565C22×C32C3×#62612yes—
566C22×C32C2×C3×D3211yescharacteristic
567C2×C3⋊D3—181no—
568C2×C3⋊D3—182no—
569C2×C3×D3—34no—
570C2×C3×D3—68no—
571C2×C3×D3—62no—
572C2×C3×D3—62no—
573C2×C3×D3—94no—
574C2×C3×D3—182no—
575C2×C3×D3—182no—
576C2×C3×D3—188no—
577C2×C3×D3—541no—
578C2×C3×D3—541no—
579C2×C3×D3—542no—
580C2×C3×D3—542no—
581C2×C3×D3—542no—
582C2×C3×D3—1082no—
583C32×C4—182no—
584C3⋊Dic3—181no—
585C3×Dic3—62no—
586C3×Dic3—182no—
587C3×Dic3—541no—
588C3×Dic3—541no—
589C3×Dic3—542no—
590C22×C9—23no—
591C22×C9—22no—
592C22×C9—22no—
593C22×C9—26no—
594C22×C9—21no—
595C22×C9—21no—
596C22×C9—22no—
597C22×C9—22no—
598C22×C9—42no—
599C22×C9—42no—
600C22×C9—46no—
601C22×C9—64no—
602C22×C9—61no—
603C22×C9—61no—
604C22×C9—62no—
605C22×C9—62no—
606C22×C9—94no—
607C22×C9—122no—
608C22×C9—121no—
609C22×C9—122no—
610C22×C9—124no—
611C22×C9—184no—
612C22×C9—188no—
613C22×C9—1816no—
614C22×C9—184no—
615C22×C9—184no—
616C22×C9—182no—
617C22×C9—182no—
618C22×C9C4⋊AGL(1,ℤ/9)12yescomplemented
619C22×C9#611⋊C312yescomplemented
620C22×C9C22×AGL(1,ℤ/9)11yescharacteristic
621C22×C9C22×AGL(1,ℤ/9)11yescharacteristic
622C2×D9—28no—
623C2×D9—22no—
624C2×D9—22no—
625C2×D9—186no—
626C2×D9—182no—
627C2×D9—182no—
628C2×D9—181no—
629C2×D9—182no—
630C2×D9—182no—
631C2×D9—181no—
632C2×D9—362no—
633C2×D9—362no—
634C2×D9—366no—
635C2×D9#611⋊C314yescomplemented
636C4×C9—182no—
637C4×C9—362no—
638Dic9—22no—
639Dic9—186no—
640Dic9—182no—
641Dic9—182no—
642Dic9—181no—
643Dic9—181no—
644#120—811noSylow
645C33#6397711yescharacteristic
6463−1+2—31no—
6473−1+2—31no—
6483−1+2—61no—
6493−1+2—61no—
6503−1+2—63no—
651C3×C9—21no—
652C3×C9—21no—
653C3×C9—21no—
654C3×C9—41no—
655C3×C9C3×#88211yescharacteristic
656C3×C9C3×#95311yescharacteristic
657C23×C3—21no—
658C23×C3—92no—
659C23×C3—91no—
660C23×C3—184no—
661C23×C3—182no—
662C23×C3—272no—
663C23×C3—542no—
664C23×C3—544no—
665C23×C3—811no—
666C23×C3D3×AGL(1,ℤ/9)11yescharacteristic
667C23×C3D3×AGL(1,ℤ/9)11yescharacteristic
668C22×D3—32no—
669C22×D3—64no—
670C22×D3—62no—
671C22×D3—271no—
672C22×D3—271no—
673C22×D3—541no—
674C3×D4—1624no—
675C3×D4—1622no—
676C2×C3×C4—92no—
677C2×C3×C4—272no—
678C2×C3×C4—811no—
679#67—544no—
680#67—544no—
681#67—542no—
682#67—542no—
683C2×Dic3—32no—
684C2×Dic3—271no—
685C2×Dic3—271no—
686C2×Dic3—541no—
687D12—544no—
688C2×C32—22no—
689C2×C32—31no—
690C2×C32—31no—
691C2×C32—32no—
692C2×C32—32no—
693C2×C32—61no—
694C2×C32—62no—
695C2×C32—62no—
696C2×C32—62no—
697C2×C32—122no—
698C2×C32—184no—
699C2×C32C2×C3×#62611yescharacteristic
700C2×C32C3×D3×#6712yes—
701C3⋊D3—361no—
702C3×D3—64no—
703C3×D3—184no—
704C3×D3—1081no—
705C3×D3—1081no—
706C3×D3—1082no—
707C2×C9—23no—
708C2×C9—26no—
709C2×C9—22no—
710C2×C9—22no—
711C2×C9—21no—
712C2×C9—21no—
713C2×C9—22no—
714C2×C9—22no—
715C2×C9—42no—
716C2×C9—42no—
717C2×C9—46no—
718C2×C9—64no—
719C2×C9—61no—
720C2×C9—61no—
721C2×C9—62no—
722C2×C9—62no—
723C2×C9—122no—
724C2×C9—122no—
725C2×C9—121no—
726C2×C9—124no—
727C2×C9—188no—
728C2×C9—184no—
729C2×C9C2×C4⋊AGL(1,ℤ/9)11yescharacteristic
730C2×C9D4×AGL(1,ℤ/9)12yes—
731C2×C9C2×#611⋊C311yescharacteristic
732C2×C9C2×#611⋊C312yes—
733D9—24no—
734D9—366no—
735D9—362no—
736D9—362no—
737D9—361no—
738D9—361no—
739C24—91no—
740C2×D4—812no—
741C2×D4—811no—
742C22⋊C4—91no—
743C22⋊C4—812no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—42no—
749C22×C3—94no—
750C22×C3—91no—
751C22×C3—92no—
752C22×C3—182no—
753C22×C3—188no—
754C22×C3—182no—
755C22×C3—182no—
756C22×C3—274no—
757C22×C3—542no—
758C22×C3—542no—
759C22×C3—548no—
760C22×C3—1621no—
761C22×C3—1622no—
762C22×C3#6192⋊C312yes—
763C22×C3#6195⋊C312yes—
764C22×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
765C22×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
766C2×D3—34no—
767C2×D3—68no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—542no—
771C2×D3—541no—
772C2×D3—541no—
773C2×D3—542no—
774C2×D3—542no—
775C2×D3—1082no—
776C3×C4—182no—
777C3×C4—542no—
778C3×C4—1621no—
779Dic3—62no—
780Dic3—542no—
781Dic3—541no—
782Dic3—541no—
783C32—31no—
784C32—31no—
785C32—61no—
786C32C3×#6397711yescharacteristic
787C9—23no—
788C9—21no—
789C9—21no—
790C9—61no—
791C9—61no—
792C9—121no—
793C9#63444⋊C311yescharacteristic, complemented
794C9#1172170411yescharacteristic, complemented
795C23—92no—
796C23—184no—
797C23—182no—
798C23—811no—
799C23#92265⋊C211yescharacteristic
800D4—1624no—
801D4—1622no—
802C2×C4—92no—
803C2×C4—811no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—22no—
807C2×C3—21no—
808C2×C3—42no—
809C2×C3—92no—
810C2×C3—91no—
811C2×C3—182no—
812C2×C3—184no—
813C2×C3—544no—
814C2×C3—3241no—
815C2×C3C2×#6192⋊C311yescharacteristic
816C2×C3C2×#6195⋊C311yescharacteristic
817C2×C3#67×AGL(1,ℤ/9)12yes—
818C2×C3D3×#611⋊C312yes—
819D3—64no—
820D3—1082no—
821D3—1081no—
822D3—1081no—
823C22—22no—
824C22—94no—
825C22—188no—
826C22—182no—
827C22—182no—
828C22—1622no—
829C22—1621no—
830C22#1451682912yescomplemented
831C22C2×#92265⋊C211yescharacteristic
832C4—182no—
833C4—1621no—
834C3—21no—
835C3—91no—
836C3#7222003111yescharacteristic
837C3#7222003311yescharacteristic
838C2—22no—
839C2—184no—
840C2—3241no—
841C2C2×#1451682911yescharacteristic
842C2#7221990412yes—
subgroupG/H
centerC22C2×#92265⋊C2
commutator, cosocleC22×C92C23×C3
Frattini, socleC22×C32C2×C3×D32
FittingC23×#6900C22
hypercenterC23#92265⋊C2
hypocenterC92C3×#120
LCSG ▷ C22×C92 ▷ C92
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
3. #72220029C3semidirect
4. #72219978C2semidirect
5. #72219969C2semidirect
6. C23×#92265C2semidirect
7. C2×#14516829C2semidirect
8. C2×#14517678C2semidirect
10. C22×#92314C22semidirect
15. C2×#11757618C22semidirect
16. C2×#11757569C22semidirect
26. C23×C9×D9C2×C3semidirect
31. C2×#10619673C2×C3semidirect
32. C2×#10619530C2×C3semidirect
34. C9×#3676C2×C3semidirect
35. (C2×D9)⋊Dic9C2×C3semidirect
37. C22×#6900D4semidirect
44. C2×#92265D4semidirect
78. C22×C9⋊D9C22×C3semidirect
86. C2×C9⋊Dic9C22×C3semidirect
88. C2×C9×Dic9C22×C3semidirect
164. C22×C92C3×D4semidirect
175. C2×C9×D9C3×D4semidirect
184. #6900#120semidirect
294. C23×D9AGL(1,ℤ/9)semidirect
311. #3676AGL(1,ℤ/9)semidirect
415. C92C3×#120semidirect
482. C2×Dic9C2×AGL(1,ℤ/9)semidirect
618. C22×C9C4⋊AGL(1,ℤ/9)semidirect
619. C22×C9#611⋊C3semidirect
635. C2×D9#611⋊C3semidirect
793. C9#63444⋊C3semidirect
794. C9#11721704semidirect
830. C22#14516829semidirect

Maximal subgroups

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

subgroupindex
#722200333
#722200313
#722200293
#722199782
#722199692
C23×#922652
C2×#145168292
C2×#145176782