Finite Group Databasebeta

← #13148402

Subgroups — #13148402

Order 1728.

1158 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
4C9×#883C211yesmaximal, characteristic, complemented
5C3×#63445C211yesmaximal, characteristic, complemented
6#11721280C211yesmaximal, characteristic, complemented
7#11721274C211yesmaximal, characteristic, complemented
8#11721269C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721020C211yesmaximal, characteristic, complemented
11#11721000C211yesmaximal, characteristic, complemented
12#11720988C211yesmaximal, characteristic, complemented
13#11720980C211yesmaximal, characteristic, complemented
14#11720954C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10594260—31nomaximal
17D9×#123—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic, complemented
26#88668—24no—
27C2×#6195C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic, complemented
34C4×D3×D9—24no—
35C3×C9×C22⋊C4C2211yescharacteristic, complemented
36#88551C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39C9×#217C2211yescharacteristic, complemented
40C3×#3676C2211yescharacteristic, complemented
41C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×C4⋊Dic3C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×C4×D32—31no—
57C22⋊C4×C3⋊D3—31no—
58C3×#883—31no—
59C3×#883D311yescharacteristic
60#63974—31no—
61#63969—31no—
62#63969—31no—
63#63921—31no—
64#63900—31no—
65#63890—31no—
66#63890—31no—
67#63883—31no—
68#63850—31no—
69#63850—31no—
70C2×D4×D9—31no—
71C22×C4×D9—31no—
72C9×#123—31no—
73#63497—31no—
74#63491—31no—
75#63456—31no—
76#63456—31no—
77C4⋊C4×D9—31no—
78C4⋊C4×D9—31no—
79#63448—31no—
80#63445—31no—
81#63445D311yescharacteristic, complemented
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9—61no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9—22no—
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2311yescharacteristic
91C22×C3⋊D9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9D414yes—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C4×C3⋊D9—22no—
102C4×C3⋊D9—22no—
103C9×#67—22no—
104C3×#611—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C4×D3×C9—22no—
112C3×C4×D9—22no—
113#6195—22no—
114D3×Dic9—22no—
115#6192—22no—
116(C3⋊D9)⋊C4—22no—
117(C3⋊D9)⋊C4—22no—
118(C3⋊D9)⋊C4—22no—
119Dic3×D9—22no—
120D3×#123—91no—
121D3×#123—91no—
122C23×C3⋊D3—31no—
123C22×D32—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C2×C3×#67C2×D311yescharacteristic
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3C2×D311yescharacteristic
130#3811—64no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#624—31no—
134C2×#624—31no—
135C2×#624—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C4×D32—64no—
139C23×D9—31no—
140C23×D9—31no—
141C23×D9—61no—
142C32×C22⋊C4C2×D311yescharacteristic
143#3757—31no—
144#3752—31no—
145#3752—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4C2×D311yescharacteristic
154#3724—31no—
155#3724—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158#3722—31no—
159#3722—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162C2×D4×C9—31no—
163C22×C4×C9—31no—
164C2×#611—31no—
165C2×#611C2×D311yescharacteristic
166C22×Dic9—31no—
167D4×D9—64no—
168C2×D36—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—64no—
176C2×C4×D9—61no—
177C2×C4×D9—61no—
178C2×C4×D9C2×D311yescharacteristic, complemented
179C9×C4⋊C4—31no—
180C9×C4⋊C4—31no—
181C9×C22⋊C4—21no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4—31no—
184C9×C22⋊C4C2×D311yescharacteristic, complemented
185#3676—31no—
186#3676—31no—
187#3676—61no—
188#3676C2×D311yescharacteristic, complemented
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—61no—
195(C2×D9)⋊C4—61no—
196(C2×D9)⋊C4C2×D311yescharacteristic, complemented
197C4⋊Dic9—31no—
198C4⋊Dic9C2×D311yescharacteristic, complemented
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×C3⋊D9—44no—
211C2×C3⋊D9C2×D412yes—
212C2×C3⋊D9#4112yes—
213C2×C3⋊D9#4112yes—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9C2×D412yes—
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9C2×D412yes—
220D3×D9—28no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C3×Dic9—21no—
231C2×D3×D4—91no—
232C2×D3×D4—91no—
233C22×C4×D3—91no—
234C22×C4×D3—91no—
235C3×#123—31no—
236C3×#123—91no—
237#935—91no—
238#935—91no—
239#929—91no—
240#929—91no—
241#894—91no—
242#894—91no—
243#894—91no—
244#894—91no—
245D3×C4⋊C4—91no—
246D3×C4⋊C4—91no—
247D3×C4⋊C4—91no—
248D3×C4⋊C4—91no—
249#886—91no—
250#886—91no—
251#883—31no—
252#883—91no—
253#883—91no—
254#883D911yescharacteristic, complemented
255D3×C22⋊C4—91no—
256D3×C22⋊C4—91no—
257D3×C22⋊C4—91no—
258D3×C22⋊C4—91no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—181no—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3×D3—31no—
269C22×C3×D3C22×D311yescharacteristic
270C2×D32—34no—
271C2×D32—62no—
272C2×D32—62no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—31no—
277C4×C3⋊D3—62no—
278C4×C3⋊D3—62no—
279C3×#67—22no—
280C3×#67—62no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287C3×C4×D3—22no—
288C3×C4×D3—62no—
289#626—62no—
290#626—62no—
291#624—62no—
292#624—62no—
293#624—62no—
294D3×Dic3—62no—
295D3×Dic3—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—31no—
300C22×D9—34no—
301C22×D9—31no—
302C22×D9—61no—
303C22×D9—61no—
304C22×D9—62no—
305C22×D9—62no—
306C22×D9—62no—
307C22×D9—62no—
308C22×D9—62no—
309C22×D9—64no—
310C22×D9—122no—
311C22×D9—122no—
312C22×D9C22×D311yescharacteristic
313D4×C9—62no—
314C2×C4×C9—21no—
315C2×C4×C9—21no—
316C2×C4×C9—31no—
317C2×C4×C9—31no—
318C2×C4×C9—31no—
319C2×C4×C9—62no—
320C2×C4×C9C22×D311yescharacteristic
321C2×C4×C9C22×D311yescharacteristic
322#611—22no—
323#611—62no—
324C2×Dic9—31no—
325C2×Dic9—31no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—62no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332D36—62no—
333C4×D9—22no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—62no—
339C4×D9—62no—
340C4×D9—122no—
341C4×D9—122no—
342C2×#123—271noSylow
343C2×C3×C9—41no—
344C2×C3×C9C22×D411yescharacteristic
345C2×C3×C9C2×#4111yescharacteristic
346C2×C3×C9C2×#4111yescharacteristic
347C3⋊D9—41no—
348C3⋊D9#12314yescomplemented
349D3×C9—22no—
350C3×D9—22no—
351C23×D3—91no—
352C23×D3—91no—
353C23×D3—91no—
354C23×D3—91no—
355C23×D3—181no—
356C2×C3×D4—31no—
357C2×C3×D4—91no—
358C22×C3×C4—31no—
359C22×C3×C4—91no—
360C2×#67—31no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67C2×D911yescharacteristic
364C22×Dic3—91no—
365C22×Dic3—91no—
366D3×D4—184no—
367D3×D4—184no—
368C2×D12—91no—
369C2×D12—91no—
370C2×C4×D3—31no—
371C2×C4×D3—91no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—181no—
384C2×C4×D3—181no—
385C2×C4×D3—184no—
386C2×C4×D3—184no—
387C2×C4×D3C2×D911yescharacteristic, complemented
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4C2×D911yescharacteristic, complemented
398C3×C22⋊C4D3211yescharacteristic
399#217—31no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—91no—
404#217—181no—
405#217C2×D911yescharacteristic, complemented
406(C2×D3)⋊C4—31no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—181no—
418(C2×D3)⋊C4—181no—
419(C2×D3)⋊C4C2×D911yescharacteristic, complemented
420C4⋊Dic3—31no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423C4⋊Dic3C2×D911yescharacteristic, complemented
424Dic3⋊C4—31no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4C2×D911yescharacteristic, complemented
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—32no—
437C2×C3⋊D3—32no—
438C2×C3⋊D3—32no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—124no—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—32no—
446C2×C3×D3—61no—
447C2×C3×D3—61no—
448C2×C3×D3D3×D412yes—
449D32—68no—
450C32×C4—21no—
451C32×C4—21no—
452C3⋊Dic3—61no—
453C3⋊Dic3—61no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—21no—
457C3×Dic3—61no—
458C3×Dic3—61no—
459C3×Dic3—61no—
460C22×C9—22no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—21no—
464C22×C9—21no—
465C22×C9—32no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9—61no—
469C22×C9—61no—
470C22×C9C23×D311yescharacteristic
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—32no—
474C2×D9—32no—
475C2×D9—32no—
476C2×D9—62no—
477C2×D9—62no—
478C2×D9—62no—
479C2×D9—68no—
480C2×D9—62no—
481C2×D9—61no—
482C2×D9—61no—
483C2×D9—61no—
484C2×D9—121no—
485C2×D9—121no—
486C2×D9—124no—
487C2×D9—128no—
488C2×D9D3×D412yes—
489C4×C9—21no—
490C4×C9—21no—
491C4×C9—41no—
492C4×C9—41no—
493C4×C9—61no—
494C4×C9—61no—
495C4×C9—61no—
496Dic9—21no—
497Dic9—21no—
498Dic9—21no—
499Dic9—61no—
500Dic9—61no—
501Dic9—121no—
502Dic9—121no—
503C22×D4—271no—
504C23×C4—271no—
505#123—31no—
506#123—91no—
507#123—271no—
508#123—271no—
509#123—271no—
510#123—271no—
511#123—271no—
512#123—271no—
513C2×C4⋊C4—271no—
514C2×C4⋊C4—271no—
515C2×C22⋊C4—271no—
516C2×C22⋊C4—271no—
517C2×C22⋊C4—271no—
518C3×C9C2×#12311yescharacteristic, complemented, Sylow
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—91no—
522C23×C3C22×D911yescharacteristic
523C23×C3C2×D3211yescharacteristic
524C22×D3—31no—
525C22×D3—94no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—94no—
529C22×D3—91no—
530C22×D3—91no—
531C22×D3—181no—
532C22×D3—181no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—182no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—182no—
542C22×D3—182no—
543C22×D3—184no—
544C22×D3—362no—
545C22×D3—362no—
546C22×D3C22×D911yescharacteristic
547C3×D4—62no—
548C3×D4—182no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—62no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—182no—
559C2×C3×C4C22×D911yescharacteristic
560C2×C3×C4C22×D911yescharacteristic
561C2×C3×C4C2×D3211yescharacteristic
562C2×C3×C4C2×D3211yescharacteristic
563#67—22no—
564#67—62no—
565#67—182no—
566#67—182no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—91no—
571C2×Dic3—91no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3—182no—
577C2×Dic3—182no—
578C2×Dic3C22×D911yescharacteristic
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581D12—182no—
582D12—182no—
583C4×D3—22no—
584C4×D3—62no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—182no—
590C4×D3—182no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—182no—
594C4×D3—182no—
595C4×D3—182no—
596C4×D3—182no—
597C4×D3—362no—
598C4×D3—362no—
599C2×C32—41no—
600C2×C32C2×D3×D411yescharacteristic
601C2×C32D3×#4111yescharacteristic
602C2×C32D3×#4111yescharacteristic
603C3⋊D3—34no—
604C3⋊D3—121no—
605C3×D3—22no—
606C3×D3—62no—
607C2×C9—21no—
608C2×C9—21no—
609C2×C9—21no—
610C2×C9—42no—
611C2×C9—41no—
612C2×C9—62no—
613C2×C9C2×D3×D411yescharacteristic
614C2×C9D3×#4111yescharacteristic
615C2×C9D3×#4111yescharacteristic
616D9—22no—
617D9—34no—
618D9—64no—
619D9—122no—
620D9—121no—
621C24—271no—
622C24—271no—
623C2×D4—31no—
624C2×D4—91no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—544no—
628C22×C4—31no—
629C22×C4—91no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—271no—
634C22×C4—271no—
635C22×C4—271no—
636C22×C4—271no—
637C22×C4—544no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—271no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4D3×D911yescharacteristic, complemented
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—32no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—92no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3C23×D911yescharacteristic
675C22×C3C22×D3211yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—32no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—92no—
682C2×D3—92no—
683C2×D3—92no—
684C2×D3—92no—
685C2×D3—92no—
686C2×D3—92no—
687C2×D3—182no—
688C2×D3—182no—
689C2×D3—182no—
690C2×D3—188no—
691C2×D3—188no—
692C2×D3—182no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—361no—
700C2×D3—361no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—368no—
704C2×D3D4×D912yes—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—181no—
715C3×C4—181no—
716C3×C4—181no—
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—181no—
724Dic3—181no—
725Dic3—181no—
726Dic3—181no—
727Dic3—361no—
728Dic3—361no—
729C32D3×#12311yescharacteristic
730C9—21no—
731C9D3×#12311yescharacteristic, complemented
732C23—31no—
733C23—91no—
734C23—274no—
735C23—271no—
736C23—271no—
737C23—542no—
738C23—542no—
739C23—542no—
740C23—542no—
741C23—542no—
742C23C2×D3×D911yescharacteristic
743D4—62no—
744D4—182no—
745D4—542no—
746D4—542no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—62no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—182no—
755C2×C4—271no—
756C2×C4—271no—
757C2×C4—542no—
758C2×C4—542no—
759C2×C4—542no—
760C2×C4—542no—
761C2×C4—542no—
762C2×C4—542no—
763C2×C4—542no—
764C2×C4C2×D3×D911yescharacteristic
765C2×C4C2×D3×D911yescharacteristic
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—62no—
773C2×C3—182no—
774C2×C3C2×D4×D911yescharacteristic
775C2×C3#41×D911yescharacteristic
776C2×C3#41×D911yescharacteristic
777C2×C3#6430611yescharacteristic
778C2×C3D32×D411yescharacteristic
779C2×C3#6431211yescharacteristic
780D3—22no—
781D3—62no—
782D3—94no—
783D3—94no—
784D3—184no—
785D3—362no—
786D3—361no—
787D3—361no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—32no—
792C22—61no—
793C22—61no—
794C22—92no—
795C22—181no—
796C22—181no—
797C22—272no—
798C22—272no—
799C22—272no—
800C22—548no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—1084no—
805C22C22×D3×D911yescharacteristic
806C4—21no—
807C4—21no—
808C4—61no—
809C4—61no—
810C4—61no—
811C4—181no—
812C4—181no—
813C4—181no—
814C4—541no—
815C4—541no—
816C3—21no—
817C3D9×#12311yescharacteristic, complemented
818C3#1059426011yescharacteristic
819C2—41no—
820C2—62no—
821C2—182no—
822C2—274no—
823C2—1081no—
824C2#1172247511yescharacteristic
825C2D3×D4×D911yescharacteristic
826C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#123
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×D9C2semidirect
3. C22⋊C4×C3⋊D9C2semidirect
4. C9×#883C2semidirect
5. C3×#63445C2semidirect
6. #11721280C2semidirect
7. #11721274C2semidirect
8. #11721269C2semidirect
9. #11721048C2semidirect
10. #11721020C2semidirect
11. #11721000C2semidirect
12. #11720988C2semidirect
13. #11720980C2semidirect
14. #11720954C2semidirect
15. #11720938C2semidirect
24. C2×C4×D3×C9C22semidirect
25. C2×C3×C4×D9C22semidirect
28. C2×D3×Dic9C22semidirect
33. C2×Dic3×D9C22semidirect
35. C3×C9×C22⋊C4C22semidirect
36. #88551C22semidirect
37. #88536C22semidirect
38. #88536C22semidirect
39. C9×#217C22semidirect
40. C3×#3676C22semidirect
41. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×C4⋊Dic3C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. #88445C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
81. #63445D3semidirect
178. C2×C4×D9C2×D3semidirect
184. C9×C22⋊C4C2×D3semidirect
188. #3676C2×D3semidirect
196. (C2×D9)⋊C4C2×D3semidirect
198. C4⋊Dic9C2×D3semidirect
202. Dic9⋊C4C2×D3semidirect
254. #883D9semidirect
348. C3⋊D9#123semidirect
387. C2×C4×D3C2×D9semidirect
397. C3×C22⋊C4C2×D9semidirect
405. #217C2×D9semidirect
419. (C2×D3)⋊C4C2×D9semidirect
423. C4⋊Dic3C2×D9semidirect
431. Dic3⋊C4C2×D9semidirect
518. C3×C9C2×#123semidirect
657. C22⋊C4D3×D9semidirect
731. C9D3×#123semidirect
817. C3D9×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×C4×D3×D92
C22⋊C4×C3⋊D92
C9×#8832
C3×#634452
#117212802
#117212742
#117212692
#117210482
#117210202
#117210002
#117209882
#117209802
#117209542
#117209382
#105942603
D9×#1233