Finite Group Databasebeta

← C2×#10589738 #11903214

Subgroups — C2×#10589738 #11903214

Order 1152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic, complemented
3C2×#63506C211yesmaximal, characteristic, complemented
4C2×C4×#611C211yesmaximal, characteristic
5C22×Dic9⋊C4C211yesmaximal, characteristic, complemented
6#10589738C2116yesmaximal, direct product factor
7C2×#63458C211yesmaximal, characteristic, complemented
8C2×#63458C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
10C2×#63451C211yesmaximal, characteristic, complemented
11C2×#63451C211yesmaximal, characteristic, complemented
12C2×#63449C211yesmaximal, characteristic, complemented
13C2×#611⋊C4C211yesmaximal, characteristic
14C2×#611⋊C4C211yesmaximal, characteristic
15C2×#63440C211yesmaximal, characteristic, complemented
16C2×#63440C211yesmaximal, characteristic, complemented
17C2×#5636—31nomaximal
18C22×Q8×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C22×#611C2211yescharacteristic
21C23×Dic9C2211yescharacteristic
22C23×Dic9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C22×C4×D9C2211yescharacteristic
26C22×Dic18C2211yescharacteristic
27C22×Dic18C2211yescharacteristic
28C9×C22⋊Q8C2218yescomplemented
29C2×C9×C4⋊C4C2211yescharacteristic
30C2×C9×C4⋊C4C2211yescharacteristic
31C2×C9×C4⋊C4C2211yescharacteristic
32C2×C9×C22⋊C4C2211yescharacteristic
33C2×C9×C22⋊C4C2211yescharacteristic
34C2×#3676C2211yescharacteristic
35#63508C2218yescomplemented
36#63506C2218yescomplemented
37C4×#611C2218yes—
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×(C2×D9)⋊C4C2211yescharacteristic
41C2×C4⋊Dic9C2211yescharacteristic
42C2×C4⋊Dic9C2211yescharacteristic
43C2×Dic9⋊C4C2211yescharacteristic
44C2×Dic9⋊C4C2211yescharacteristic
45C2×Dic9⋊C4C2211yescharacteristic
46C2×Dic9⋊C4C2211yescharacteristic
47C2×Dic9⋊C4C2211yescharacteristic
48C2×Dic9⋊C4C2211yescharacteristic
49C2×Dic9⋊C4C2211yescharacteristic
50C2×Dic9⋊C4C2211yescharacteristic
51C2×Dic9⋊C4C2211yescharacteristic
52C2×Dic9⋊C4C2211yescharacteristic
53C2×Dic9⋊C4C2211yescharacteristic
54C2×Dic9⋊C4C2218yescomplemented
55C2×C4×Dic9C2211yescharacteristic
56C2×C4×Dic9C2211yescharacteristic
57C2×C4×Dic9C2211yescharacteristic
58#63458C2218yescomplemented
59#63458C2218yescomplemented
60C4⋊C4×D9C2218yescomplemented
61#63451C2218yescomplemented
62#63451C2218yescomplemented
63#63449C2218yescomplemented
64#611⋊C4C2218yes—
65#611⋊C4C2218yes—
66#63440C2218yescomplemented
67#63440C2218yescomplemented
68C2×C3×C22⋊Q8D311yescharacteristic
69C2×#946—31no—
70C2×#944—31no—
71C2×C4×#67—31no—
72C22×Dic3⋊C4—31no—
73#5636—316no—
74C2×#896—31no—
75C2×#896—31no—
76C2×D3×C4⋊C4—31no—
77C2×#889—31no—
78C2×#889—31no—
79C2×#887—31no—
80C2×#67⋊C4—31no—
81C2×#67⋊C4—31no—
82C2×#878—31no—
83C2×#878—31no—
84C24×C9C2311yescharacteristic
85C23×D9C2311yescharacteristic
86C2×Q8×C9—42no—
87C2×Q8×C9C2314yes—
88C22×C4×C9—42no—
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C22×C4×C9C2311yescharacteristic
95C22×C4×C9C2314yes—
96C2×#611Q818yescomplemented
97C2×#611C2314yes—
98C22×Dic9—24no—
99C22×Dic9—42no—
100C22×Dic9C2311yescharacteristic
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C22×Dic9C2311yescharacteristic
104C22×Dic9C2314yes—
105C22×Dic9C2311yescharacteristic
106C22×Dic9C2314yes—
107C22×Dic9C2311yescharacteristic
108C22×Dic9C2311yescharacteristic
109C2×C4×D9—24no—
110C2×C4×D9—42no—
111C2×C4×D9—42no—
112C2×C4×D9C2314yes—
113C2×C4×D9C2314yes—
114C2×C4×D9C2314yes—
115C2×Dic18—24no—
116C2×Dic18—42no—
117C2×Dic18C2314yes—
118C2×Dic18C2314yes—
119C9×C4⋊C4C2314yes—
120C9×C4⋊C4C2314yes—
121C9×C4⋊C4C2314yes—
122C9×C22⋊C4C2314yes—
123C9×C22⋊C4C2314yes—
124#3676C2314yes—
125(C2×D9)⋊C4C2314yes—
126(C2×D9)⋊C4C2314yes—
127(C2×D9)⋊C4C2314yes—
128C4⋊Dic9C2314yes—
129C4⋊Dic9C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134Dic9⋊C4C2314yes—
135Dic9⋊C4C2314yes—
136Dic9⋊C4C2314yes—
137Dic9⋊C4C2314yes—
138Dic9⋊C4C2314yes—
139Dic9⋊C4C2314yes—
140Dic9⋊C4C2314yes—
141C4×Dic9C2314yes—
142C4×Dic9C2314yes—
143C4×Dic9C2314yes—
144C2×#554—91noSylow
145C22×C3×Q8C2×D311yescharacteristic
146C23×C3×C4C2×D311yescharacteristic
147C22×#67—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—31no—
153C22×Dic6—31no—
154C22×Dic6—31no—
155C3×C22⋊Q8C2×D318yes—
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C4⋊C4C2×D311yescharacteristic
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×#217—31no—
162#946—38no—
163#944—38no—
164C4×#67—38no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×Dic3⋊C4—38no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—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×Dic3⋊C4—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185#896—38no—
186#896—38no—
187D3×C4⋊C4—38no—
188#889—38no—
189#889—38no—
190#887—38no—
191#67⋊C4—38no—
192#67⋊C4—38no—
193#878—38no—
194#878—38no—
195C23×C9—22no—
196C23×C9—22no—
197C23×C9C2×Q814yes—
198C23×C9C2412yes—
199C23×C9C2411yescharacteristic
200C22×D9—22no—
201C22×D9—22no—
202C22×D9C2×Q814yes—
203C22×D9C2412yes—
204Q8×C9—44no—
205C2×C4×C9—22no—
206C2×C4×C9—22no—
207C2×C4×C9—22no—
208C2×C4×C9—22no—
209C2×C4×C9—22no—
210C2×C4×C9—22no—
211C2×C4×C9—44no—
212C2×C4×C9C2412yes—
213C2×C4×C9C2412yes—
214C2×C4×C9C2412yes—
215C2×C4×C9C2412yes—
216C2×C4×C9C2412yes—
217C2×C4×C9C2412yes—
218#611C2×Q8116yescomplemented
219C2×Dic9—22no—
220C2×Dic9—22no—
221C2×Dic9—22no—
222C2×Dic9—22no—
223C2×Dic9—22no—
224C2×Dic9—28no—
225C2×Dic9—44no—
226C2×Dic9C2×Q814yes—
227C2×Dic9#4114yes—
228C2×Dic9C2412yes—
229C2×Dic9C2412yes—
230C2×Dic9C2412yes—
231C2×Dic9C2412yes—
232C2×Dic9C2412yes—
233C2×Dic9C2412yes—
234C2×Dic9C2412yes—
235C4×D9—28no—
236C4×D9—44no—
237C4×D9—44no—
238Dic18—28no—
239Dic18—44no—
240#554—916no—
241C2×C4⋊Q8—91no—
242C2×#125—91no—
243C2×#125—91no—
244C2×C22⋊Q8—91no—
245C2×C22⋊Q8—91no—
246C2×C22⋊Q8—91no—
247C2×C22⋊Q8—91no—
248C2×C22⋊Q8—91no—
249C2×C22⋊Q8D911yescharacteristic, complemented
250C2×C4×Q8—91no—
251C2×C4×D4—91no—
252C2×C4×D4—91no—
253C2×C4×D4—91no—
254C22×C4⋊C4—91no—
255C22×C4⋊C4—91no—
256C24×C3C22×D311yescharacteristic
257C23×D3—31no—
258C2×C3×Q8—42no—
259C2×C3×Q8C22×D314yes—
260C22×C3×C4—42no—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C22×C3×C4C22×D311yescharacteristic
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D314yes—
268C2×#67—38no—
269C2×#67—34no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—34no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—34no—
279C22×Dic3—64no—
280C22×Dic3—122no—
281C2×C4×D3—34no—
282C2×C4×D3—34no—
283C2×C4×D3—34no—
284C2×C4×D3—64no—
285C2×C4×D3—122no—
286C2×C4×D3—122no—
287C2×Dic6—34no—
288C2×Dic6—34no—
289C2×Dic6—64no—
290C2×Dic6—122no—
291C3×C4⋊C4C22×D314yes—
292C3×C4⋊C4C22×D314yes—
293C3×C4⋊C4C22×D314yes—
294C3×C22⋊C4C22×D314yes—
295C3×C22⋊C4C22×D314yes—
296#217—34no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302Dic3⋊C4—34no—
303Dic3⋊C4—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—
312Dic3⋊C4—34no—
313C4×Dic3—34no—
314C4×Dic3—34no—
315C4×Dic3—34no—
316C22×C9—28no—
317C22×C9—22no—
318C22×C9—22no—
319C22×C9C22×Q814yes—
320C22×C9C22×Q812yes—
321C22×C9C2×#4112yes—
322C22×C9H(5,𝔽2)12yes—
323C22×C9C2511yescharacteristic
324C2×D9—28no—
325C2×D9—22no—
326C2×D9—22no—
327C2×D9C22×Q814yes—
328C4×C9—22no—
329C4×C9—22no—
330C4×C9—22no—
331C4×C9—22no—
332C4×C9—22no—
333C4×C9—22no—
334Dic9—22no—
335Dic9—22no—
336Dic9—22no—
337Dic9—22no—
338Dic9—22no—
339Dic9C22×Q814yes—
340Dic9C2×#4114yes—
341C22×Q8—91no—
342C22×Q8—91no—
343C22×Q8C2×D911yescharacteristic
344C22×D4—91no—
345C23×C4—91no—
346C23×C4—91no—
347C23×C4—91no—
348C23×C4—91no—
349C23×C4—91no—
350C23×C4C2×D911yescharacteristic
351C4⋊Q8—98no—
352#125—98no—
353#125—98no—
354C22⋊Q8—98no—
355C22⋊Q8—98no—
356C22⋊Q8—98no—
357C22⋊Q8—98no—
358C22⋊Q8—98no—
359C22⋊Q8C2×D918yescomplemented
360C4×Q8—98no—
361C4×D4—98no—
362C4×D4—98no—
363C4×D4—98no—
364C2×C4⋊C4—91no—
365C2×C4⋊C4—91no—
366C2×C4⋊C4—91no—
367C2×C4⋊C4—91no—
368C2×C4⋊C4—91no—
369C2×C4⋊C4—91no—
370C2×C4⋊C4—98no—
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×C4⋊C4—91no—
378C2×C4⋊C4—98no—
379C2×C4⋊C4C2×D911yescharacteristic
380C2×C4⋊C4C2×D911yescharacteristic
381C2×C4⋊C4C2×D911yescharacteristic
382C2×C22⋊C4—91no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4C2×D911yescharacteristic
387C2×C22⋊C4C2×D911yescharacteristic
388C2×C42—91no—
389C2×C42—91no—
390C2×C42—91no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3D3×Q814yes—
394C23×C3C23×D312yes—
395C23×C3C23×D311yescharacteristic
396C22×D3—34no—
397C22×D3—32no—
398C22×D3—62no—
399C22×D3—62no—
400C3×Q8—44no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—44no—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414#67—316no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—68no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—124no—
431C4×D3—68no—
432C4×D3—124no—
433C4×D3—124no—
434Dic6—68no—
435Dic6—124no—
436C2×C9—24no—
437C2×C9#55414yescomplemented
438C2×C9C23×Q811yescharacteristic
439C2×C9C22×#4111yescharacteristic
440C2×C9C2×H(5,𝔽2)11yescharacteristic
441D9—24no—
442C24—91no—
443C24C22×D911yescharacteristic
444C2×Q8—42no—
445C2×Q8—94no—
446C2×Q8—94no—
447C2×Q8—184no—
448C2×Q8—362no—
449C2×Q8C22×D914yes—
450C2×D4—98no—
451C2×D4—94no—
452C22×C4—42no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—94no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—94no—
462C22×C4—94no—
463C22×C4—94no—
464C22×C4—94no—
465C22×C4—184no—
466C22×C4—184no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4—362no—
470C22×C4C22×D911yescharacteristic
471C22×C4C22×D911yescharacteristic
472C22×C4C22×D911yescharacteristic
473C22×C4C22×D911yescharacteristic
474C22×C4C22×D911yescharacteristic
475C22×C4C22×D911yescharacteristic
476C22×C4C22×D914yes—
477C4⋊C4—94no—
478C4⋊C4—94no—
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—
489C4⋊C4—94no—
490C4⋊C4C22×D914yes—
491C4⋊C4C22×D914yes—
492C4⋊C4C22×D914yes—
493C22⋊C4—94no—
494C22⋊C4—94no—
495C22⋊C4—94no—
496C22⋊C4—94no—
497C22⋊C4C22×D914yes—
498C22⋊C4C22×D914yes—
499C42—94no—
500C42—94no—
501C42—94no—
502C22×C3—28no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3#100412yes—
506C22×C3C2×D3×Q814yes—
507C22×C3C2×D3×Q812yes—
508C22×C3D3×#4112yes—
509C22×C3C24×D311yescharacteristic
510C2×D3—34no—
511C2×D3—68no—
512C2×D3—62no—
513C2×D3—62no—
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—22no—
520Dic3—34no—
521Dic3—34no—
522Dic3—62no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—62no—
527C9C2×#55411yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—92no—
531C23—94no—
532C23—182no—
533C23—182no—
534C23Q8×D914yes—
535C23C23×D912yes—
536C23C23×D911yescharacteristic
537Q8—44no—
538Q8—188no—
539Q8—364no—
540D4—916no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—44no—
548C2×C4—92no—
549C2×C4—92no—
550C2×C4—94no—
551C2×C4—94no—
552C2×C4—92no—
553C2×C4—92no—
554C2×C4—92no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—188no—
558C2×C4—188no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—364no—
565C2×C4—364no—
566C2×C4—364no—
567C2×C4C23×D912yes—
568C2×C4C23×D912yes—
569C2×C4C23×D912yes—
570C2×C4C23×D912yes—
571C2×C4C23×D912yes—
572C2×C4C23×D912yes—
573C2×C3—24no—
574C2×C3#563614yes—
575C2×C3C2×#100411yescharacteristic
576C2×C3C22×D3×Q811yescharacteristic
577C2×C3C2×D3×#4111yescharacteristic
578D3—64no—
579C22—28no—
580C22—22no—
581C22—22no—
582C22—94no—
583C22—188no—
584C22—182no—
585C22—182no—
586C22#6371012yes—
587C22C2×Q8×D914yes—
588C22C2×Q8×D912yes—
589C22#41×D912yes—
590C22C24×D911yescharacteristic
591C4—22no—
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—22no—
597C4—94no—
598C4—94no—
599C4—182no—
600C4—182no—
601C4—182no—
602C4—182no—
603C4—182no—
604C3C2×#563611yescharacteristic
605C2—24no—
606C2—184no—
607C2#1058973814yesdirect product factor
608C2C2×#6371011yescharacteristic
609C2C22×Q8×D911yescharacteristic
610C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×C22⋊Q8C2
socleC23×C3C23×D3
prime radicalC22×#611C22
hypercenterC2×C22⋊Q8D9
hypocenterC9C2×#554
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C9×C22⋊Q8C2semidirect
2. C2×#63508C2semidirect
3. C2×#63506C2semidirect
5. C22×Dic9⋊C4C2semidirect
6. #10589738C2direct (N × H)
7. C2×#63458C2semidirect
8. C2×#63458C2semidirect
9. C2×C4⋊C4×D9C2semidirect
10. C2×#63451C2semidirect
11. C2×#63451C2semidirect
12. C2×#63449C2semidirect
15. C2×#63440C2semidirect
16. C2×#63440C2semidirect
28. C9×C22⋊Q8C22semidirect
35. #63508C22semidirect
36. #63506C22semidirect
54. C2×Dic9⋊C4C22semidirect
58. #63458C22semidirect
59. #63458C22semidirect
60. C4⋊C4×D9C22semidirect
61. #63451C22semidirect
62. #63451C22semidirect
63. #63449C22semidirect
66. #63440C22semidirect
67. #63440C22semidirect
96. C2×#611Q8semidirect
218. #611C2×Q8semidirect
249. C2×C22⋊Q8D9semidirect
359. C22⋊Q8C2×D9semidirect
437. C2×C9#554semidirect
527. C9C2×#554semidirect
607. C2#10589738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊Q82
C2×#635082
C2×#635062
C2×C4×#6112
C22×Dic9⋊C42
#105897382
C2×#634582
C2×C4⋊C4×D92
C2×#634512
C2×#634492
C2×#611⋊C42
C2×#634402
C2×#56363