Finite Group Databasebeta

← C2×#10589771 #11901608

Subgroups — C2×#10589771 #11901608

Order 1152.

1698 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#124C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic, complemented
3C2×#63506C211yesmaximal, characteristic, complemented
4C2×#63501C211yesmaximal, characteristic
5C2×#63497C211yesmaximal, characteristic, complemented
6#10589771C2116yesmaximal, direct product factor
7C2×#63447C211yesmaximal, characteristic, complemented
8C2×#63447C211yesmaximal, characteristic, complemented
9C2×#63445C211yesmaximal, characteristic, complemented
10C2×#611⋊C4C211yesmaximal, characteristic, complemented
11C2×#63441C211yesmaximal, characteristic, complemented
12C2×#63440C211yesmaximal, characteristic, complemented
13C2×#63440C211yesmaximal, characteristic, complemented
14C2×#63439C211yesmaximal, characteristic, complemented
15C2×#63438C211yesmaximal, characteristic, complemented
16C2×C4×Dic18C211yesmaximal, characteristic, complemented
17C2×#5669—31nomaximal
18C22×Q8×C9C2211yescharacteristic
19C22×D4×C9C2211yescharacteristic
20C22×#611C2211yescharacteristic
21C22×#611C2211yescharacteristic
22C23×Dic9C2211yescharacteristic
23C23×Dic9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C22×Dic18C2211yescharacteristic
26C22×Dic18C2211yescharacteristic
27C9×#124C2218yescomplemented
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic
30C2×C9×C22⋊C4C2211yescharacteristic
31C2×C9×C22⋊C4C2211yescharacteristic
32C2×C42×C9C2211yescharacteristic
33C2×#3676C2211yescharacteristic
34C2×#3676C2211yescharacteristic
35C2×#3676C2211yescharacteristic
36C2×#3676C2211yescharacteristic
37#63508C2218yescomplemented
38#63506C2218yescomplemented
39#63501C2218yes—
40#63497C2218yescomplemented
41C2×(C2×D9)⋊C4C2211yescharacteristic
42C2×(C2×D9)⋊C4C2211yescharacteristic
43C2×(C2×D9)⋊C4C2211yescharacteristic
44C2×(C2×D9)⋊C4C2211yescharacteristic
45C2×C4⋊Dic9C2211yescharacteristic
46C2×C4⋊Dic9C2211yescharacteristic
47C2×Dic9⋊C4C2211yescharacteristic
48C2×Dic9⋊C4C2211yescharacteristic
49C2×Dic9⋊C4C2211yescharacteristic
50C2×Dic9⋊C4C2211yescharacteristic
51C2×Dic9⋊C4C2211yescharacteristic
52C2×Dic9⋊C4C2211yescharacteristic
53C2×Dic9⋊C4C2211yescharacteristic
54C2×Dic9⋊C4C2211yescharacteristic
55C2×C4×Dic9C2211yescharacteristic
56C2×C4×Dic9C2211yescharacteristic
57C2×C4×Dic9C2211yescharacteristic
58#63447C2218yescomplemented
59#63447C2218yescomplemented
60#63445C2218yescomplemented
61#611⋊C4C2218yescomplemented
62#63441C2218yescomplemented
63#63440C2218yescomplemented
64#63440C2218yescomplemented
65#63439C2218yescomplemented
66#63438C2218yescomplemented
67C4×Dic18C2218yescomplemented
68C2×C3×#124D311yescharacteristic
69C2×#946—31no—
70C2×#944—31no—
71C2×#939—31no—
72C2×#935—31no—
73#5669—316no—
74C2×#885—31no—
75C2×#885—31no—
76C2×#883—31no—
77C2×#67⋊C4—31no—
78C2×#879—31no—
79C2×#878—31no—
80C2×#878—31no—
81C2×#877—31no—
82C2×#876—31no—
83C2×C4×Dic6—31no—
84C24×C9C2311yescharacteristic
85C24×C9C2311yescharacteristic
86C23×D9C2311yescharacteristic
87C2×Q8×C9—42no—
88C2×Q8×C9C2314yes—
89C2×D4×C9—42no—
90C2×D4×C9C2314yes—
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C22×C4×C9C2311yescharacteristic
95C22×C4×C9C2311yescharacteristic
96C2×#611—24no—
97C2×#611—42no—
98C2×#611C2314yes—
99C2×#611C2314yes—
100C22×Dic9—24no—
101C22×Dic9—42no—
102C22×Dic9C2311yescharacteristic
103C22×Dic9C2311yescharacteristic
104C22×Dic9C2311yescharacteristic
105C22×Dic9C2311yescharacteristic
106C22×Dic9C2314yes—
107C22×Dic9C2311yescharacteristic
108C22×Dic9C2311yescharacteristic
109C22×Dic9C2314yes—
110C22×Dic9C2311yescharacteristic
111C2×C4×D9—42no—
112C2×C4×D9C2314yes—
113C2×Dic18—24no—
114C2×Dic18—42no—
115C2×Dic18C2314yes—
116C2×Dic18C2314yes—
117C9×C22⋊C4C2314yes—
118C9×C22⋊C4C2314yes—
119C9×C22⋊C4C2314yes—
120C9×C22⋊C4C2314yes—
121C42×C9C2314yes—
122#3676C2314yes—
123#3676C2314yes—
124#3676C2314yes—
125#3676C2314yes—
126(C2×D9)⋊C4C2314yes—
127(C2×D9)⋊C4C2314yes—
128(C2×D9)⋊C4C2314yes—
129(C2×D9)⋊C4C2314yes—
130C4⋊Dic9C2314yes—
131C4⋊Dic9C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2314yes—
136Dic9⋊C4C2314yes—
137Dic9⋊C4C2314yes—
138Dic9⋊C4C2314yes—
139Dic9⋊C4C2314yes—
140C4×Dic9C2314yes—
141C4×Dic9C2314yes—
142C4×Dic9C2314yes—
143C2×#542—91noSylow
144C22×C3×Q8C2×D311yescharacteristic
145C22×C3×D4C2×D311yescharacteristic
146C22×#67—31no—
147C22×#67—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×C4×D3—31no—
151C22×Dic6—31no—
152C22×Dic6—31no—
153C3×#124C2×D318yes—
154C2×C3×C22⋊C4C2×D311yescharacteristic
155C2×C3×C22⋊C4C2×D311yescharacteristic
156C2×C3×C22⋊C4C2×D311yescharacteristic
157C2×C3×C22⋊C4C2×D311yescharacteristic
158C2×C3×C42C2×D311yescharacteristic
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163#946—38no—
164#944—38no—
165#939—38no—
166#935—38no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184#885—38no—
185#885—38no—
186#883—38no—
187#67⋊C4—38no—
188#879—38no—
189#878—38no—
190#878—38no—
191#877—38no—
192#876—38no—
193C4×Dic6—38no—
194C23×C9—22no—
195C23×C9—22no—
196C23×C9—22no—
197C23×C9—22no—
198C23×C9—22no—
199C23×C9—22no—
200C23×C9C2412yes—
201C23×C9C2412yes—
202C23×C9C2411yescharacteristic
203C22×D9—22no—
204C22×D9—22no—
205C22×D9—22no—
206C22×D9C2412yes—
207Q8×C9—44no—
208D4×C9—44no—
209C2×C4×C9—22no—
210C2×C4×C9—22no—
211C2×C4×C9—22no—
212C2×C4×C9—22no—
213C2×C4×C9—22no—
214C2×C4×C9C2412yes—
215C2×C4×C9C2412yes—
216C2×C4×C9C2412yes—
217C2×C4×C9C2412yes—
218C2×C4×C9C2412yes—
219#611—28no—
220#611—44no—
221C2×Dic9—22no—
222C2×Dic9—22no—
223C2×Dic9—22no—
224C2×Dic9—22no—
225C2×Dic9—22no—
226C2×Dic9—22no—
227C2×Dic9—28no—
228C2×Dic9—44no—
229C2×Dic9#4114yes—
230C2×Dic9C2412yes—
231C2×Dic9C2412yes—
232C2×Dic9C2412yes—
233C2×Dic9C2412yes—
234C2×Dic9C2412yes—
235C2×Dic9C2412yes—
236C2×Dic9C2412yes—
237C4×D9—44no—
238Dic18—28no—
239Dic18—44no—
240#542—916no—
241C2×C4⋊Q8—91no—
242C2×#126—91no—
243C2×#126—91no—
244C2×#124—91no—
245C2×#124—91no—
246C2×#124D911yescharacteristic, complemented
247C2×#123—91no—
248C2×#123—91no—
249C2×C22⋊Q8—91no—
250C2×C22⋊Q8—91no—
251C2×C22⋊Q8—91no—
252C2×#121—91no—
253C2×C4×Q8—91no—
254C2×C4×D4—91no—
255C2×#117—91no—
256C24×C3C22×D311yescharacteristic
257C24×C3C22×D311yescharacteristic
258C23×D3—31no—
259C2×C3×Q8—42no—
260C2×C3×Q8C22×D314yes—
261C2×C3×D4—42no—
262C2×C3×D4C22×D314yes—
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C2×#67—34no—
269C2×#67—34no—
270C2×#67—64no—
271C2×#67—122no—
272C22×Dic3—31no—
273C22×Dic3—34no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—31no—
280C22×Dic3—34no—
281C22×Dic3—64no—
282C22×Dic3—122no—
283C2×C4×D3—34no—
284C2×C4×D3—122no—
285C2×Dic6—34no—
286C2×Dic6—34no—
287C2×Dic6—64no—
288C2×Dic6—122no—
289C3×C22⋊C4C22×D314yes—
290C3×C22⋊C4C22×D314yes—
291C3×C22⋊C4C22×D314yes—
292C3×C22⋊C4C22×D314yes—
293C3×C42C22×D314yes—
294#217—34no—
295#217—34no—
296#217—34no—
297#217—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—34no—
301(C2×D3)⋊C4—34no—
302C4⋊Dic3—34no—
303C4⋊Dic3—34no—
304Dic3⋊C4—34no—
305Dic3⋊C4—34no—
306Dic3⋊C4—34no—
307Dic3⋊C4—34no—
308Dic3⋊C4—34no—
309Dic3⋊C4—34no—
310Dic3⋊C4—34no—
311Dic3⋊C4—34no—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—34no—
315C22×C9—22no—
316C22×C9—22no—
317C22×C9—22no—
318C22×C9—22no—
319C22×C9—22no—
320C22×C9—22no—
321C22×C9—44no—
322C22×C9—44no—
323C22×C9C2×#4112yes—
324C22×C9H(5,𝔽2)12yes—
325C22×C92−1+412yes—
326C22×C9C2511yescharacteristic
327C2×D9—22no—
328C2×D9—22no—
329C2×D9—22no—
330C2×D9—44no—
331C4×C9—22no—
332C4×C9—22no—
333C4×C9—22no—
334C4×C9—22no—
335C4×C9—22no—
336Dic9—22no—
337Dic9—22no—
338Dic9—22no—
339Dic9—22no—
340Dic9—22no—
341Dic9—22no—
342Dic9C2×#4114yes—
343C22×Q8—91no—
344C22×Q8—91no—
345C22×Q8C2×D911yescharacteristic
346C22×D4—91no—
347C22×D4—91no—
348C22×D4C2×D911yescharacteristic
349C23×C4—91no—
350C23×C4—91no—
351C23×C4—91no—
352C4⋊Q8—98no—
353#126—98no—
354#126—98no—
355#124—98no—
356#124—98no—
357#124C2×D918yescomplemented
358#123—98no—
359#123—98no—
360C22⋊Q8—98no—
361C22⋊Q8—98no—
362C22⋊Q8—98no—
363#121—98no—
364C4×Q8—98no—
365C4×D4—98no—
366#117—98no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—91no—
371C2×C4⋊C4—91no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—91no—
377C2×C22⋊C4—91no—
378C2×C22⋊C4—91no—
379C2×C22⋊C4—91no—
380C2×C22⋊C4—91no—
381C2×C22⋊C4—91no—
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4C2×D911yescharacteristic
386C2×C22⋊C4C2×D911yescharacteristic
387C2×C22⋊C4C2×D911yescharacteristic
388C2×C22⋊C4C2×D911yescharacteristic
389C2×C42—91no—
390C2×C42—91no—
391C2×C42—91no—
392C2×C42C2×D911yescharacteristic
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3C23×D312yes—
400C23×C3C23×D312yes—
401C23×C3C23×D311yescharacteristic
402C22×D3—32no—
403C22×D3—62no—
404C22×D3—62no—
405C22×D3—62no—
406C3×Q8—44no—
407C3×D4—44no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418#67—68no—
419#67—124no—
420C2×Dic3—34no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—68no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—124no—
436C4×D3—124no—
437Dic6—68no—
438Dic6—124no—
439C2×C9—42no—
440C2×C9—42no—
441C2×C9#54214yescomplemented
442C2×C9C22×#4111yescharacteristic
443C2×C9C2×H(5,𝔽2)11yescharacteristic
444C2×C9C2×2−1+411yescharacteristic
445D9—42no—
446C24—91no—
447C24C22×D911yescharacteristic
448C24C22×D911yescharacteristic
449C2×Q8—42no—
450C2×Q8—94no—
451C2×Q8—94no—
452C2×Q8—184no—
453C2×Q8—362no—
454C2×Q8C22×D914yes—
455C2×D4—42no—
456C2×D4—94no—
457C2×D4—94no—
458C2×D4—184no—
459C2×D4—362no—
460C2×D4C22×D914yes—
461C22×C4—91no—
462C22×C4—94no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—94no—
470C22×C4—94no—
471C22×C4—184no—
472C22×C4—362no—
473C22×C4—362no—
474C22×C4C22×D911yescharacteristic
475C22×C4C22×D911yescharacteristic
476C22×C4C22×D911yescharacteristic
477C22×C4C22×D911yescharacteristic
478C22×C4C22×D911yescharacteristic
479C4⋊C4—94no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C4⋊C4—94no—
483C4⋊C4—94no—
484C4⋊C4—94no—
485C4⋊C4—94no—
486C4⋊C4—94no—
487C4⋊C4—94no—
488C4⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—94no—
491C22⋊C4—94no—
492C22⋊C4—94no—
493C22⋊C4—94no—
494C22⋊C4—94no—
495C22⋊C4—94no—
496C22⋊C4—94no—
497C22⋊C4C22×D914yes—
498C22⋊C4C22×D914yes—
499C22⋊C4C22×D914yes—
500C22⋊C4C22×D914yes—
501C42—94no—
502C42—94no—
503C42—94no—
504C42C22×D914yes—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3#100412yes—
514C22×C3D3×#4112yes—
515C22×C3#101012yes—
516C22×C3C24×D311yescharacteristic
517C2×D3—62no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—124no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—22no—
526Dic3—34no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—62no—
531Dic3—62no—
532Dic3—62no—
533C9C2×#54211yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—92no—
541C23—182no—
542C23—182no—
543C23—182no—
544C23C23×D912yes—
545C23C23×D912yes—
546C23C23×D911yescharacteristic
547Q8—44no—
548Q8—188no—
549Q8—364no—
550D4—44no—
551D4—188no—
552D4—364no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—92no—
559C2×C4—94no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—188no—
567C2×C4—182no—
568C2×C4—182no—
569C2×C4—182no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—364no—
574C2×C4—364no—
575C2×C4C23×D912yes—
576C2×C4C23×D912yes—
577C2×C4C23×D912yes—
578C2×C4C23×D912yes—
579C2×C4C23×D912yes—
580C2×C3—42no—
581C2×C3—42no—
582C2×C3#566914yes—
583C2×C3C2×#100411yescharacteristic
584C2×C3C2×D3×#4111yescharacteristic
585C2×C3C2×#101011yescharacteristic
586D3—122no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—44no—
594C22—44no—
595C22—182no—
596C22—182no—
597C22—182no—
598C22—364no—
599C22#6371012yes—
600C22#41×D912yes—
601C22#6371612yes—
602C22C24×D911yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—22no—
607C4—22no—
608C4—94no—
609C4—182no—
610C4—182no—
611C4—182no—
612C4—182no—
613C4—182no—
614C4—182no—
615C3C2×#566911yescharacteristic
616C2—42no—
617C2—42no—
618C2—362no—
619C2#1058977114yesdirect product factor
620C2C2×#6371011yescharacteristic
621C2C2×#41×D911yescharacteristic
622C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#124C2
socleC23×C3C23×D3
prime radicalC2×#63501C2
hypercenterC2×#124D9
hypocenterC9C2×#542
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C9×#124C2semidirect
2. C2×#63508C2semidirect
3. C2×#63506C2semidirect
5. C2×#63497C2semidirect
6. #10589771C2direct (N × H)
7. C2×#63447C2semidirect
8. C2×#63447C2semidirect
9. C2×#63445C2semidirect
10. C2×#611⋊C4C2semidirect
11. C2×#63441C2semidirect
12. C2×#63440C2semidirect
13. C2×#63440C2semidirect
14. C2×#63439C2semidirect
15. C2×#63438C2semidirect
16. C2×C4×Dic18C2semidirect
27. C9×#124C22semidirect
37. #63508C22semidirect
38. #63506C22semidirect
40. #63497C22semidirect
58. #63447C22semidirect
59. #63447C22semidirect
60. #63445C22semidirect
61. #611⋊C4C22semidirect
62. #63441C22semidirect
63. #63440C22semidirect
64. #63440C22semidirect
65. #63439C22semidirect
66. #63438C22semidirect
67. C4×Dic18C22semidirect
246. C2×#124D9semidirect
357. #124C2×D9semidirect
441. C2×C9#542semidirect
533. C9C2×#542semidirect
619. C2#10589771direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1242
C2×#635082
C2×#635062
C2×#635012
C2×#634972
#105897712
C2×#634472
C2×#634452
C2×#611⋊C42
C2×#634412
C2×#634402
C2×#634392
C2×#634382
C2×C4×Dic182
C2×#56693