Finite Group Databasebeta

← #13150968

Subgroups — #13150968

Order 1728.

1120 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88662C211yesmaximal, characteristic, complemented
2C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
3#11721837C211yesmaximal, characteristic, complemented
4C9×#939C211yesmaximal, characteristic, complemented
5C3×D4×Dic9C211yesmaximal, characteristic, complemented
6#11721291C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#11721275C211yesmaximal, characteristic, complemented
9#11721262C211yesmaximal, characteristic, complemented
10#11721249C211yesmaximal, characteristic, complemented
11#11721241C211yesmaximal, characteristic, complemented
12#11721013C211yesmaximal, characteristic, complemented
13#11720995C211yesmaximal, characteristic, complemented
14#11720958C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10595138—31nomaximal
17#10589708—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C22×C9×Dic3C2211yescharacteristic
25C22×C3×Dic9C2211yescharacteristic
26C22×C3×Dic9C2211yescharacteristic, complemented
27C2×#6195C2211yescharacteristic
28C2×#6195C2211yescharacteristic
29#88662—24no—
30C2×D3×Dic9C2211yescharacteristic, complemented
31C2×(C3⋊D9)⋊C4—24no—
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×(C3⋊D9)⋊C4C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×#6189C2211yescharacteristic, complemented
37#88551C2211yescharacteristic
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic
42C3×#3676C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×C4×Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×#624—31no—
56C2×#3804—31no—
57#64146—31no—
58C3×#939D311yescharacteristic
59C3×D4×Dic3—31no—
60#63981—31no—
61#63975—31no—
62Dic3×#67—31no—
63#63964—31no—
64#63958—31no—
65#63952—31no—
66#63895—31no—
67#63880—31no—
68#63854—31no—
69#63836—31no—
70C2×#3699—31no—
71C22×C4×D9—31no—
72C9×#121—31no—
73#63500—31no—
74#63499—31no—
75#63499—31no—
76#63499—61no—
77D4×Dic9—31no—
78D4×Dic9D311yescharacteristic, complemented
79#63486—31no—
80#63459—31no—
81#63454—31no—
82#63445—31no—
83#63445—31no—
84#611⋊C4—31no—
85#611⋊C4—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9—22no—
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C3×D4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97#6233—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C9×#67—22no—
101C9×#67—22no—
102C2×C9×Dic3—22no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9—22no—
107C2×C3×Dic9—22no—
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112#6195—22no—
113#6195—22no—
114D3×Dic9—22no—
115(C3⋊D9)⋊C4—22no—
116(C3⋊D9)⋊C4—22no—
117(C3⋊D9)⋊C4—22no—
118(C3⋊D9)⋊C4D414yescomplemented
119#6189—22no—
120#5606—91no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C2×C32×D4C2×D311yescharacteristic
124C2×#638—31no—
125C2×#638—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×#67C2×D311yescharacteristic
128C22×C3×Dic3—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3C2×D311yescharacteristic
131C2×#627—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#624—31no—
135C2×#624—31no—
136C2×#624—31no—
137C2×#624—31no—
138C2×#624—64no—
139#3804—64no—
140C2×D3×Dic3—31no—
141C23×D9—31no—
142C23×D9—61no—
143#3757—31no—
144#3752—31no—
145#3752—31no—
146C3×#217—31no—
147C3×#217—31no—
148C3×#217C2×D311yescharacteristic
149C3×(C2×D3)⋊C4C2×D311yescharacteristic
150C3×C4⋊Dic3—31no—
151C3×Dic3⋊C4C2×D311yescharacteristic
152C3×C4×Dic3—31no—
153#3724—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157#3722—31no—
158#3722—31no—
159(C2×D3)⋊Dic3—31no—
160Dic32—31no—
161C2×D4×C9—21no—
162C2×D4×C9—31no—
163C2×D4×C9—31no—
164C2×D4×C9C2×D311yescharacteristic
165C22×C4×C9—31no—
166C2×#611—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—61no—
171C2×#611—61no—
172C22×Dic9—31no—
173C22×Dic9C2×D311yescharacteristic
174C22×Dic9C2×D311yescharacteristic, complemented
175#3699—64no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—64no—
181C2×Dic18—31no—
182C9×C4⋊C4—31no—
183C9×C22⋊C4—31no—
184C9×C22⋊C4—31no—
185#3676—31no—
186#3676—31no—
187#3676—61no—
188#3676C2×D311yescharacteristic
189#3676C2×D311yescharacteristic, complemented
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—
196C4⋊Dic9—31no—
197C4⋊Dic9—31no—
198C4⋊Dic9C2×D311yescharacteristic, complemented
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201C4×Dic9—31no—
202C4×Dic9C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9#4112yescomplemented
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—28no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9C2×D412yes—
216C2×C3⋊D9#4112yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C3×C4×C9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C9×Dic3—21no—
224C9×Dic3—21no—
225C9×Dic3C2×D412yes—
226C3×Dic9—21no—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9C2×D412yes—
230C2×#237—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×#121—31no—
235C3×C4×D4—91no—
236#939D911yescharacteristic, complemented
237#938—91no—
238#937—91no—
239#937—91no—
240#937—91no—
241#937—181no—
242D4×Dic3—31no—
243D4×Dic3—91no—
244C4×#67—91no—
245C4×#67—91no—
246#924—91no—
247#897—91no—
248#896—91no—
249#894—91no—
250#892—91no—
251#884—91no—
252#883—91no—
253#883—91no—
254#883—91no—
255#882—91no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
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×D3C22×D311yescharacteristic
269C32×D4—22no—
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272#638—62no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C3×#67—22no—
276C3×#67—22no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287#627—62no—
288#626—62no—
289#626—62no—
290#624—34no—
291#624—62no—
292#624—62no—
293#624—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C23×C9C22×D311yescharacteristic
300C22×D9—31no—
301C22×D9—31no—
302C22×D9—61no—
303C22×D9—61no—
304C22×D9—62no—
305C22×D9—62no—
306C22×D9—62no—
307C22×D9—122no—
308C22×D9—122no—
309C22×D9—122no—
310D4×C9—22no—
311D4×C9—42no—
312D4×C9—62no—
313D4×C9—62no—
314C2×C4×C9—21no—
315C2×C4×C9—31no—
316C2×C4×C9—31no—
317C2×C4×C9—31no—
318C2×C4×C9—62no—
319C2×C4×C9C22×D311yescharacteristic
320#611—62no—
321#611—62no—
322#611—62no—
323#611—62no—
324#611—122no—
325#611—122no—
326C2×Dic9—22no—
327C2×Dic9—22no—
328C2×Dic9—31no—
329C2×Dic9—31no—
330C2×Dic9—61no—
331C2×Dic9—61no—
332C2×Dic9—62no—
333C2×Dic9C22×D311yescharacteristic
334C2×Dic9C22×D311yescharacteristic
335C2×Dic9C22×D311yescharacteristic
336C2×Dic9C22×D311yescharacteristic
337C4×D9—34no—
338C4×D9—62no—
339C4×D9—62no—
340C4×D9—62no—
341Dic18—62no—
342#525—271noSylow
343C2×C3×C9—22no—
344C2×C3×C9—41no—
345C2×C3×C9C22×D411yescharacteristic
346C2×C3×C9C2×#4111yescharacteristic
347C2×C3×C9C2×#4111yescharacteristic
348C3⋊D9—22no—
349C3⋊D9—22no—
350D3×C9—41no—
351C23×D3—91no—
352C23×D3—91no—
353C23×D3—181no—
354C2×C3×D4—21no—
355C2×C3×D4—31no—
356C2×C3×D4—31no—
357C2×C3×D4C2×D911yescharacteristic
358C2×C3×D4D3211yescharacteristic
359C22×C3×C4—31no—
360C22×C3×C4—91no—
361C22×C3×C4—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—181no—
369C2×#67—181no—
370C2×#67C2×D911yescharacteristic
371C2×#67C2×D911yescharacteristic, complemented
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—91no—
375C22×Dic3C2×D911yescharacteristic
376#237—184no—
377#235—184no—
378C2×D12—91no—
379C2×D12—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—184no—
390C2×C4×D3—184no—
391C2×Dic6—91no—
392C2×Dic6—91no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—91no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C42—91no—
400#217—31no—
401#217—31no—
402#217—91no—
403#217—91no—
404#217—91no—
405#217—181no—
406#217C2×D911yescharacteristic, complemented
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—181no—
417(C2×D3)⋊C4—181no—
418(C2×D3)⋊C4C2×D911yescharacteristic, complemented
419C4⋊Dic3—31no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4C2×D911yescharacteristic, complemented
429C4×Dic3—31no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32#23712yes—
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—32no—
440C2×C3⋊D3—32no—
441C2×C3⋊D3—68no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C32×C4—21no—
450C3⋊Dic3—61no—
451C3⋊Dic3—61no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—32no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C3×Dic3—61no—
458C3×Dic3D3×D412yes—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—21no—
464C22×C9—21no—
465C22×C9—22no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9—41no—
469C22×C9—41no—
470C22×C9—41no—
471C22×C9—61no—
472C22×C9—61no—
473C22×C9—61no—
474C22×C9#23512yescomplemented
475C22×C9C23×D311yescharacteristic
476C2×D9—32no—
477C2×D9—32no—
478C2×D9—62no—
479C2×D9—62no—
480C2×D9—68no—
481C2×D9—61no—
482C2×D9—61no—
483C2×D9—61no—
484C2×D9—61no—
485C2×D9—121no—
486C2×D9—121no—
487C2×D9—121no—
488C2×D9—121no—
489C2×D9—128no—
490C4×C9—21no—
491C4×C9—32no—
492C4×C9—41no—
493C4×C9—61no—
494C4×C9—61no—
495Dic9—21no—
496Dic9—21no—
497Dic9—21no—
498Dic9—61no—
499Dic9—61no—
500Dic9—121no—
501Dic9—121no—
502Dic9D3×D412yes—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—271no—
508C22⋊Q8—271no—
509#121—31no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—91no—
514C4×D4—271no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C3×C9#52511yescharacteristic, complemented, Sylow
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—31no—
522C23×C3C22×D911yescharacteristic
523C23×C3C22×D911yescharacteristic
524C23×C3C2×D3211yescharacteristic
525C23×C3C2×D3211yescharacteristic
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—181no—
531C22×D3—181no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—362no—
539C22×D3—362no—
540C22×D3—362no—
541C22×D3C22×D911yescharacteristic
542C3×D4—22no—
543C3×D4—22no—
544C3×D4—42no—
545C3×D4—62no—
546C3×D4—62no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—62no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—182no—
557C2×C3×C4—182no—
558C2×C3×C4C22×D911yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560#67—22no—
561#67—22no—
562#67—182no—
563#67—182no—
564#67—182no—
565#67—182no—
566#67—182no—
567#67—182no—
568#67—362no—
569#67—362no—
570C2×Dic3—22no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—91no—
578C2×Dic3—91no—
579C2×Dic3—91no—
580C2×Dic3—91no—
581C2×Dic3—181no—
582C2×Dic3—181no—
583C2×Dic3—182no—
584C2×Dic3C22×D911yescharacteristic
585C2×Dic3C22×D911yescharacteristic
586C2×Dic3C22×D911yescharacteristic
587D12—182no—
588D12—182no—
589C4×D3—94no—
590C4×D3—94no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—182no—
594C4×D3—182no—
595C4×D3—182no—
596C4×D3—182no—
597C4×D3—182no—
598Dic6—182no—
599Dic6—182no—
600C2×C32—22no—
601C2×C32—41no—
602C2×C32C2×D3×D411yescharacteristic
603C2×C32C2×#23711yescharacteristic
604C2×C32D3×#4111yescharacteristic
605C3⋊D3—62no—
606C3⋊D3—62no—
607C3×D3—41no—
608C2×C9—22no—
609C2×C9—21no—
610C2×C9—21no—
611C2×C9—21no—
612C2×C9—42no—
613C2×C9—41no—
614C2×C9—81no—
615C2×C9—121no—
616C2×C9C2×#23511yescharacteristic
617C2×C9C2×D3×D411yescharacteristic
618C2×C9D3×#4111yescharacteristic
619D9—62no—
620D9—62no—
621D9—122no—
622D9—122no—
623C24—271no—
624#41—544no—
625C2×Q8—271no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4D3×D911yescharacteristic
633C22×C4—31no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—271no—
641C22×C4—544no—
642C4⋊C4—31no—
643C4⋊C4—91no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—31no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C42—91no—
659C42—271no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3#369912yescomplemented
681C22×C3C23×D911yescharacteristic
682C22×C3#380412yes—
683C22×C3C22×D3211yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—92no—
688C2×D3—92no—
689C2×D3—92no—
690C2×D3—92no—
691C2×D3—182no—
692C2×D3—182no—
693C2×D3—188no—
694C2×D3—188no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—361no—
704C2×D3—361no—
705C2×D3—361no—
706C2×D3—361no—
707C2×D3—368no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—32no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—92no—
715C3×C4—181no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—32no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—181no—
725Dic3—181no—
726Dic3—181no—
727Dic3—181no—
728Dic3—361no—
729Dic3—361no—
730Dic3D4×D912yes—
731C32#560611yescharacteristic
732C9—21no—
733C9#554711yescharacteristic, complemented
734C23—31no—
735C23—271no—
736C23—271no—
737C23—542no—
738C23—542no—
739C23—542no—
740C23C2×D3×D911yescharacteristic
741C23C2×D3×D911yescharacteristic
742Q8—542no—
743D4—22no—
744D4—62no—
745D4—62no—
746D4—542no—
747D4—542no—
748D4—542no—
749D4—542no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—62no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—182no—
759C2×C4—182no—
760C2×C4—274no—
761C2×C4—271no—
762C2×C4—271no—
763C2×C4—542no—
764C2×C4—542no—
765C2×C4—542no—
766C2×C4—542no—
767C2×C4C2×D3×D911yescharacteristic
768C2×C3—22no—
769C2×C3—22no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—42no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—81no—
777C2×C3—121no—
778C2×C3C2×D4×D911yescharacteristic
779C2×C3C2×#369911yescharacteristic
780C2×C3#41×D911yescharacteristic
781C2×C3D32×D411yescharacteristic
782C2×C3#6431211yescharacteristic
783C2×C3C2×#380411yescharacteristic
784D3—41no—
785D3—182no—
786D3—182no—
787D3—182no—
788D3—182no—
789D3—362no—
790D3—362no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—272no—
800C22—272no—
801C22—548no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22#8866212yescomplemented
807C22C22×D3×D911yescharacteristic
808C4—21no—
809C4—32no—
810C4—61no—
811C4—61no—
812C4—92no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—541no—
817C4—541no—
818C3—21no—
819C3#1058970811yescharacteristic, complemented
820C3#1059513811yescharacteristic
821C2—22no—
822C2—41no—
823C2—121no—
824C2—542no—
825C2—542no—
826C2D3×D4×D911yescharacteristic
827C2#1172249811yescharacteristic
828C2C2×#8866211yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88662C2semidirect
2. C22×(C3⋊D9)⋊C4C2semidirect
3. #11721837C2semidirect
4. C9×#939C2semidirect
5. C3×D4×Dic9C2semidirect
6. #11721291C2semidirect
7. #67×Dic9C2semidirect
8. #11721275C2semidirect
9. #11721262C2semidirect
10. #11721249C2semidirect
11. #11721241C2semidirect
12. #11721013C2semidirect
13. #11720995C2semidirect
14. #11720958C2semidirect
15. #11720899C2semidirect
23. C2×C9×#67C22semidirect
26. C22×C3×Dic9C22semidirect
30. C2×D3×Dic9C22semidirect
36. C2×#6189C22semidirect
40. C9×#217C22semidirect
42. C3×#3676C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×C4×Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
78. D4×Dic9D3semidirect
118. (C3⋊D9)⋊C4D4semidirect
174. C22×Dic9C2×D3semidirect
189. #3676C2×D3semidirect
198. C4⋊Dic9C2×D3semidirect
202. C4×Dic9C2×D3semidirect
208. C22×C3×C9#41semidirect
216. C2×C3⋊D9#41semidirect
236. #939D9semidirect
371. C2×#67C2×D9semidirect
406. #217C2×D9semidirect
418. (C2×D3)⋊C4C2×D9semidirect
428. Dic3⋊C4C2×D9semidirect
474. C22×C9#235semidirect
518. C3×C9#525semidirect
680. C22×C3#3699semidirect
733. C9#5547semidirect
806. C22#88662semidirect
819. C3#10589708semidirect

Maximal subgroups

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

subgroupindex
C2×#886622
C22×(C3⋊D9)⋊C42
#117218372
C9×#9392
C3×D4×Dic92
#117212912
#67×Dic92
#117212752
#117212622
#117212492
#117212412
#117210132
#117209952
#117209582
#117208992
#105951383
#105897083