Finite Group Databasebeta

← C2×#10589703 #11903091

Subgroups — C2×#10589703 #11903091

Order 1152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#121C211yesmaximal, characteristic, complemented
2C2×#63501C211yesmaximal, characteristic, complemented
3C2×#63501C211yesmaximal, characteristic, complemented
4C2×#63501C211yesmaximal, characteristic, complemented
5C2×#63497C211yesmaximal, characteristic, complemented
6C2×D4×Dic9C211yesmaximal, characteristic, complemented
7C2×D4×Dic9C211yesmaximal, characteristic, complemented
8C2×C4×#611C211yesmaximal, characteristic, complemented
9C22×Dic9⋊C4C211yesmaximal, characteristic, complemented
10#10589703C2116yesmaximal, direct product factor
11C2×#63460C211yesmaximal, characteristic, complemented
12C2×#63451C211yesmaximal, characteristic, complemented
13C2×#63445C211yesmaximal, characteristic, complemented
14C2×#611⋊C4C211yesmaximal, characteristic, complemented
15C2×#63441C211yesmaximal, characteristic, complemented
16C2×#63439C211yesmaximal, characteristic, complemented
17C2×#5601—31nomaximal
18C22×D4×C9C2211yescharacteristic
19C22×D4×C9C2211yescharacteristic
20C22×D4×C9C2211yescharacteristic
21C23×C4×C9C2211yescharacteristic
22C22×#611C2211yescharacteristic
23C22×#611C2211yescharacteristic
24C22×#611C2211yescharacteristic
25C23×Dic9C2211yescharacteristic
26C23×Dic9C2211yescharacteristic
27C23×Dic9C2211yescharacteristic
28C23×Dic9C2211yescharacteristic
29C22×C4×D9C2211yescharacteristic
30C9×#121C2218yescomplemented
31C2×C9×C4⋊C4C2211yescharacteristic
32C2×C9×C22⋊C4C2211yescharacteristic
33C2×C9×C22⋊C4C2211yescharacteristic
34C2×#3676C2211yescharacteristic
35C2×#3676C2211yescharacteristic
36C2×#3676C2211yescharacteristic
37C2×#3676C2211yescharacteristic
38C2×#3676C2211yescharacteristic
39#63501C2218yescomplemented
40#63501C2218yescomplemented
41#63501C2218yescomplemented
42#63497C2218yescomplemented
43D4×Dic9C2218yescomplemented
44D4×Dic9C2218yescomplemented
45C4×#611C2218yescomplemented
46C2×(C2×D9)⋊C4C2211yescharacteristic
47C2×(C2×D9)⋊C4C2211yescharacteristic
48C2×(C2×D9)⋊C4C2211yescharacteristic
49C2×C4⋊Dic9C2211yescharacteristic
50C2×C4⋊Dic9C2211yescharacteristic
51C2×Dic9⋊C4C2211yescharacteristic
52C2×Dic9⋊C4C2211yescharacteristic
53C2×Dic9⋊C4C2211yescharacteristic
54C2×Dic9⋊C4C2211yescharacteristic
55C2×Dic9⋊C4C2211yescharacteristic
56C2×Dic9⋊C4C2211yescharacteristic
57C2×Dic9⋊C4C2211yescharacteristic
58C2×Dic9⋊C4C2218yescomplemented
59C2×C4×Dic9C2211yescharacteristic
60C2×C4×Dic9C2211yescharacteristic
61C2×C4×Dic9C2211yescharacteristic
62#63460C2218yescomplemented
63#63451C2218yescomplemented
64#63445C2218yescomplemented
65#611⋊C4C2218yescomplemented
66#63441C2218yescomplemented
67#63439C2218yescomplemented
68C2×C3×#121D311yescharacteristic
69C2×#939—31no—
70C2×#939—31no—
71C2×#939—31no—
72C2×#935—31no—
73C2×D4×Dic3—31no—
74C2×D4×Dic3—31no—
75C2×C4×#67—31no—
76C22×Dic3⋊C4—31no—
77#5601—316no—
78C2×#898—31no—
79C2×#889—31no—
80C2×#883—31no—
81C2×#67⋊C4—31no—
82C2×#879—31no—
83C2×#877—31no—
84C24×C9C2311yescharacteristic
85C24×C9C2311yescharacteristic
86C24×C9C2311yescharacteristic
87C23×D9C2311yescharacteristic
88C2×D4×C9—24no—
89C2×D4×C9—24no—
90C2×D4×C9—42no—
91C2×D4×C9C2314yes—
92C2×D4×C9C2314yes—
93C2×D4×C9C2314yes—
94C22×C4×C9—42no—
95C22×C4×C9C2311yescharacteristic
96C22×C4×C9C2311yescharacteristic
97C22×C4×C9C2311yescharacteristic
98C22×C4×C9C2311yescharacteristic
99C22×C4×C9C2314yes—
100C2×#611—24no—
101C2×#611—24no—
102C2×#611—42no—
103C2×#611C2314yes—
104C2×#611C2314yes—
105C2×#611C2314yes—
106C22×Dic9—24no—
107C22×Dic9—24no—
108C22×Dic9—42no—
109C22×Dic9—42no—
110C22×Dic9C2311yescharacteristic
111C22×Dic9C2311yescharacteristic
112C22×Dic9C2311yescharacteristic
113C22×Dic9C2314yes—
114C22×Dic9C2314yes—
115C22×Dic9C2311yescharacteristic
116C22×Dic9C2311yescharacteristic
117C22×Dic9C2311yescharacteristic
118C22×Dic9C2314yes—
119C22×Dic9C2314yes—
120C22×Dic9C2311yescharacteristic
121C2×C4×D9—42no—
122C2×C4×D9C2314yes—
123C9×C4⋊C4C2314yes—
124C9×C22⋊C4C2314yes—
125C9×C22⋊C4C2314yes—
126#3676C2314yes—
127#3676C2314yes—
128#3676C2314yes—
129#3676C2314yes—
130#3676C2314yes—
131(C2×D9)⋊C4C2314yes—
132(C2×D9)⋊C4C2314yes—
133(C2×D9)⋊C4C2314yes—
134C4⋊Dic9C2314yes—
135C4⋊Dic9C2314yes—
136Dic9⋊C4C2314yes—
137Dic9⋊C4C2314yes—
138Dic9⋊C4C2314yes—
139Dic9⋊C4C2314yes—
140Dic9⋊C4C2314yes—
141Dic9⋊C4C2314yes—
142Dic9⋊C4C2314yes—
143C4×Dic9C2314yes—
144C4×Dic9C2314yes—
145C4×Dic9C2314yes—
146C2×#553—91noSylow
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C22×C3×D4C2×D311yescharacteristic
150C23×C3×C4C2×D311yescharacteristic
151C22×#67—31no—
152C22×#67—31no—
153C22×#67—31no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C22×C4×D3—31no—
159C3×#121C2×D318yes—
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C2×D311yescharacteristic
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168#939—38no—
169#939—38no—
170#939—38no—
171#935—38no—
172D4×Dic3—38no—
173D4×Dic3—38no—
174C4×#67—38no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—38no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191#898—38no—
192#889—38no—
193#883—38no—
194#67⋊C4—38no—
195#879—38no—
196#877—38no—
197C23×C9—22no—
198C23×C9—22no—
199C23×C9—22no—
200C23×C9—22no—
201C23×C9—22no—
202C23×C9—22no—
203C23×C9—22no—
204C23×C9—22no—
205C23×C9#4114yes—
206C23×C9C2412yes—
207C23×C9C2412yes—
208C23×C9C2412yes—
209C23×C9C2411yescharacteristic
210C22×D9—22no—
211C22×D9—22no—
212C22×D9—22no—
213C22×D9C2412yes—
214D4×C9—28no—
215D4×C9—28no—
216D4×C9—44no—
217C2×C4×C9—22no—
218C2×C4×C9—22no—
219C2×C4×C9—22no—
220C2×C4×C9—22no—
221C2×C4×C9—44no—
222C2×C4×C9C2412yes—
223C2×C4×C9C2412yes—
224C2×C4×C9C2412yes—
225C2×C4×C9C2412yes—
226#611—28no—
227#611—28no—
228#611—44no—
229C2×Dic9—22no—
230C2×Dic9—22no—
231C2×Dic9—22no—
232C2×Dic9—22no—
233C2×Dic9—22no—
234C2×Dic9—22no—
235C2×Dic9—28no—
236C2×Dic9—28no—
237C2×Dic9—44no—
238C2×Dic9—44no—
239C2×Dic9#4114yes—
240C2×Dic9C2412yes—
241C2×Dic9C2412yes—
242C2×Dic9C2412yes—
243C2×Dic9C2412yes—
244C2×Dic9C2412yes—
245C2×Dic9C2412yes—
246C2×Dic9C2412yes—
247C4×D9—44no—
248#553—916no—
249C2×#126—91no—
250C2×#126—91no—
251C2×#125—91no—
252C2×#123—91no—
253C2×#123—91no—
254C2×#121—91no—
255C2×#121—91no—
256C2×#121—91no—
257C2×#121D911yescharacteristic, complemented
258C2×C4×D4—91no—
259C2×C4×D4—91no—
260C2×C4×D4—91no—
261C2×C4×D4—91no—
262C2×#117—91no—
263C22×C4⋊C4—91no—
264C24×C3C22×D311yescharacteristic
265C24×C3C22×D311yescharacteristic
266C24×C3C22×D311yescharacteristic
267C23×D3—31no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—42no—
271C2×C3×D4C22×D314yes—
272C2×C3×D4C22×D314yes—
273C2×C3×D4C22×D314yes—
274C22×C3×C4—42no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D314yes—
280C2×#67—34no—
281C2×#67—34no—
282C2×#67—34no—
283C2×#67—64no—
284C2×#67—64no—
285C2×#67—122no—
286C22×Dic3—31no—
287C22×Dic3—34no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—34no—
295C22×Dic3—34no—
296C22×Dic3—34no—
297C22×Dic3—64no—
298C22×Dic3—64no—
299C22×Dic3—122no—
300C22×Dic3—122no—
301C2×C4×D3—34no—
302C2×C4×D3—122no—
303C3×C4⋊C4C22×D314yes—
304C3×C22⋊C4C22×D314yes—
305C3×C22⋊C4C22×D314yes—
306#217—34no—
307#217—34no—
308#217—34no—
309#217—34no—
310#217—34no—
311(C2×D3)⋊C4—34no—
312(C2×D3)⋊C4—34no—
313(C2×D3)⋊C4—34no—
314C4⋊Dic3—34no—
315C4⋊Dic3—34no—
316Dic3⋊C4—34no—
317Dic3⋊C4—34no—
318Dic3⋊C4—34no—
319Dic3⋊C4—34no—
320Dic3⋊C4—34no—
321Dic3⋊C4—34no—
322Dic3⋊C4—34no—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C22×C9—28no—
327C22×C9—22no—
328C22×C9—22no—
329C22×C9—22no—
330C22×C9—22no—
331C22×C9—22no—
332C22×C9—22no—
333C22×C9—22no—
334C22×C9—22no—
335C22×C9—44no—
336C22×C9—44no—
337C22×C9C2×#4114yes—
338C22×C9C2×#4112yes—
339C22×C9C2×#4112yes—
340C22×C9H(5,𝔽2)12yes—
341C22×C9C2511yescharacteristic
342C2×D9—22no—
343C2×D9—22no—
344C2×D9—22no—
345C2×D9—44no—
346C4×C9—22no—
347C4×C9—22no—
348C4×C9—22no—
349C4×C9—22no—
350Dic9—22no—
351Dic9—22no—
352Dic9—22no—
353Dic9—22no—
354Dic9—22no—
355Dic9—22no—
356Dic9C2×#4114yes—
357C22×D4—91no—
358C22×D4—91no—
359C22×D4—91no—
360C22×D4C2×D911yescharacteristic
361C22×D4C2×D911yescharacteristic
362C22×D4C2×D911yescharacteristic
363C23×C4—91no—
364C23×C4—91no—
365C23×C4—91no—
366C23×C4—91no—
367C23×C4—91no—
368C23×C4C2×D911yescharacteristic
369#126—98no—
370#126—98no—
371#125—98no—
372#123—98no—
373#123—98no—
374#121—98no—
375#121—98no—
376#121—98no—
377#121C2×D918yescomplemented
378C4×D4—98no—
379C4×D4—98no—
380C4×D4—98no—
381C4×D4—98no—
382#117—98no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
387C2×C4⋊C4—98no—
388C2×C4⋊C4—91no—
389C2×C4⋊C4—91no—
390C2×C4⋊C4—91no—
391C2×C4⋊C4—91no—
392C2×C4⋊C4—91no—
393C2×C4⋊C4C2×D911yescharacteristic
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—91no—
400C2×C22⋊C4—91no—
401C2×C22⋊C4—91no—
402C2×C22⋊C4C2×D911yescharacteristic
403C2×C22⋊C4C2×D911yescharacteristic
404C2×C42—91no—
405C2×C42—91no—
406C2×C42—91no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3#23714yes—
416C23×C3C23×D312yes—
417C23×C3C23×D312yes—
418C23×C3C23×D312yes—
419C23×C3C23×D311yescharacteristic
420C22×D3—32no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C3×D4—28no—
425C3×D4—28no—
426C3×D4—44no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—44no—
432C2×C3×C4C23×D312yes—
433C2×C3×C4C23×D312yes—
434C2×C3×C4C23×D312yes—
435C2×C3×C4C23×D312yes—
436#67—68no—
437#67—68no—
438#67—124no—
439C2×Dic3—34no—
440C2×Dic3—32no—
441C2×Dic3—32no—
442C2×Dic3—32no—
443C2×Dic3—32no—
444C2×Dic3—32no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—68no—
448C2×Dic3—68no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—124no—
456C2×Dic3—124no—
457C4×D3—124no—
458C2×C9—24no—
459C2×C9—42no—
460C2×C9—42no—
461C2×C9#55314yescomplemented
462C2×C9C22×#4111yescharacteristic
463C2×C9C22×#4111yescharacteristic
464C2×C9C2×H(5,𝔽2)11yescharacteristic
465D9—42no—
466C24—91no—
467C24C22×D911yescharacteristic
468C24C22×D911yescharacteristic
469C24C22×D911yescharacteristic
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—42no—
473C2×D4—94no—
474C2×D4—94no—
475C2×D4—94no—
476C2×D4—184no—
477C2×D4—184no—
478C2×D4—362no—
479C2×D4C22×D914yes—
480C2×D4C22×D914yes—
481C2×D4C22×D914yes—
482C22×C4—42no—
483C22×C4—91no—
484C22×C4—94no—
485C22×C4—94no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—91no—
491C22×C4—91no—
492C22×C4—94no—
493C22×C4—94no—
494C22×C4—94no—
495C22×C4—184no—
496C22×C4—184no—
497C22×C4—362no—
498C22×C4—362no—
499C22×C4—362no—
500C22×C4C22×D911yescharacteristic
501C22×C4C22×D911yescharacteristic
502C22×C4C22×D911yescharacteristic
503C22×C4C22×D911yescharacteristic
504C22×C4C22×D914yes—
505C4⋊C4—94no—
506C4⋊C4—94no—
507C4⋊C4—94no—
508C4⋊C4—94no—
509C4⋊C4—94no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4—94no—
513C4⋊C4—94no—
514C4⋊C4C22×D914yes—
515C22⋊C4—94no—
516C22⋊C4—94no—
517C22⋊C4—94no—
518C22⋊C4—94no—
519C22⋊C4—94no—
520C22⋊C4—94no—
521C22⋊C4—94no—
522C22⋊C4—94no—
523C22⋊C4C22×D914yes—
524C22⋊C4C22×D914yes—
525C42—94no—
526C42—94no—
527C42—94no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—28no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3C2×#23714yes—
540C22×C3C2×#23712yes—
541C22×C3#100412yes—
542C22×C3D3×#4112yes—
543C22×C3C24×D311yescharacteristic
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—124no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—22no—
551C3×C4—22no—
552Dic3—34no—
553Dic3—62no—
554Dic3—62no—
555Dic3—62no—
556Dic3—62no—
557Dic3—62no—
558Dic3—62no—
559C9C2×#55311yescharacteristic, complemented, Sylow
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—92no—
569C23—182no—
570C23—182no—
571C23—182no—
572C23#369914yes—
573C23C23×D912yes—
574C23C23×D912yes—
575C23C23×D912yes—
576C23C23×D911yescharacteristic
577D4—28no—
578D4—28no—
579D4—44no—
580D4—188no—
581D4—188no—
582D4—364no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—44no—
588C2×C4—92no—
589C2×C4—94no—
590C2×C4—92no—
591C2×C4—92no—
592C2×C4—92no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—92no—
596C2×C4—188no—
597C2×C4—188no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4—182no—
604C2×C4—364no—
605C2×C4—364no—
606C2×C4—364no—
607C2×C4C23×D912yes—
608C2×C4C23×D912yes—
609C2×C4C23×D912yes—
610C2×C4C23×D912yes—
611C2×C3—24no—
612C2×C3—42no—
613C2×C3—42no—
614C2×C3#560114yes—
615C2×C3C22×#23711yescharacteristic
616C2×C3C2×#100411yescharacteristic
617C2×C3C2×D3×#4111yescharacteristic
618D3—122no—
619C22—28no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—44no—
629C22—44no—
630C22—182no—
631C22—182no—
632C22—182no—
633C22—364no—
634C22C2×#369914yes—
635C22C2×#369912yes—
636C22#6371012yes—
637C22#41×D912yes—
638C22C24×D911yescharacteristic
639C4—22no—
640C4—22no—
641C4—22no—
642C4—22no—
643C4—94no—
644C4—182no—
645C4—182no—
646C4—182no—
647C4—182no—
648C4—182no—
649C4—182no—
650C3C2×#560111yescharacteristic
651C2—24no—
652C2—42no—
653C2—42no—
654C2—362no—
655C2#1058970314yesdirect product factor
656C2C22×#369911yescharacteristic
657C2C2×#6371011yescharacteristic
658C2C2×#41×D911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#121C2
socleC23×C3C23×D3
hypercenterC2×#121D9
hypocenterC9C2×#553
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C9×#121C2semidirect
2. C2×#63501C2semidirect
3. C2×#63501C2semidirect
4. C2×#63501C2semidirect
5. C2×#63497C2semidirect
6. C2×D4×Dic9C2semidirect
7. C2×D4×Dic9C2semidirect
8. C2×C4×#611C2semidirect
9. C22×Dic9⋊C4C2semidirect
10. #10589703C2direct (N × H)
11. C2×#63460C2semidirect
12. C2×#63451C2semidirect
13. C2×#63445C2semidirect
14. C2×#611⋊C4C2semidirect
15. C2×#63441C2semidirect
16. C2×#63439C2semidirect
30. C9×#121C22semidirect
39. #63501C22semidirect
40. #63501C22semidirect
41. #63501C22semidirect
42. #63497C22semidirect
43. D4×Dic9C22semidirect
44. D4×Dic9C22semidirect
45. C4×#611C22semidirect
58. C2×Dic9⋊C4C22semidirect
62. #63460C22semidirect
63. #63451C22semidirect
64. #63445C22semidirect
65. #611⋊C4C22semidirect
66. #63441C22semidirect
67. #63439C22semidirect
257. C2×#121D9semidirect
377. #121C2×D9semidirect
461. C2×C9#553semidirect
559. C9C2×#553semidirect
655. C2#10589703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1212
C2×#635012
C2×#634972
C2×D4×Dic92
C2×C4×#6112
C22×Dic9⋊C42
#105897032
C2×#634602
C2×#634512
C2×#634452
C2×#611⋊C42
C2×#634412
C2×#634392
C2×#56013