Finite Group Databasebeta

← C2×#10589804 #11903350

Subgroups — C2×#10589804 #11903350

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#126C211yesmaximal, characteristic, complemented
2#10589804C2116yesmaximal, direct product factor
3C2×#63460C211yesmaximal, characteristic, complemented
4C2×#63460C211yesmaximal, characteristic, complemented
5C2×#63458C211yesmaximal, characteristic, complemented
6C2×#63450C211yesmaximal, characteristic, complemented
7C2×#63449C211yesmaximal, characteristic, complemented
8C2×#63449C211yesmaximal, characteristic, complemented
9C2×#63447C211yesmaximal, characteristic
10C2×#63447C211yesmaximal, characteristic
11C2×#611⋊C4C211yesmaximal, characteristic
12C2×#63441C211yesmaximal, characteristic, complemented
13C2×#63440C211yesmaximal, characteristic, complemented
14C2×#63439C211yesmaximal, characteristic, complemented
15C2×#63434C211yesmaximal, characteristic, complemented
16C2×C4×Dic18C211yesmaximal, characteristic, complemented
17C2×#5702—31nomaximal
18C22×#611C2211yescharacteristic
19C23×Dic9C2211yescharacteristic
20C22×C4×D9C2211yescharacteristic
21C22×Dic18C2211yescharacteristic
22C22×Dic18C2211yescharacteristic
23C22×Dic18C2211yescharacteristic
24C9×#126C2218yescomplemented
25C2×C9×C4⋊C4C2211yescharacteristic
26C2×C9×C4⋊C4C2211yescharacteristic
27C2×C9×C4⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic
30C2×C9×C22⋊C4C2211yescharacteristic
31C2×C42×C9C2211yescharacteristic
32C2×#3676C2211yescharacteristic
33C2×#3676C2211yescharacteristic
34C2×(C2×D9)⋊C4C2211yescharacteristic
35C2×(C2×D9)⋊C4C2211yescharacteristic
36C2×(C2×D9)⋊C4C2211yescharacteristic
37C2×(C2×D9)⋊C4C2211yescharacteristic
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×C4⋊Dic9C2211yescharacteristic
40C2×C4⋊Dic9C2211yescharacteristic
41C2×Dic9⋊C4C2211yescharacteristic
42C2×Dic9⋊C4C2211yescharacteristic
43C2×Dic9⋊C4C2211yescharacteristic
44C2×Dic9⋊C4C2211yescharacteristic
45C2×Dic9⋊C4C2211yescharacteristic
46C2×Dic9⋊C4C2211yescharacteristic
47C2×Dic9⋊C4C2211yescharacteristic
48C2×C4×Dic9C2211yescharacteristic
49C2×C4×Dic9C2211yescharacteristic
50C2×C4×Dic9C2211yescharacteristic
51C2×C4×Dic9C2211yescharacteristic
52C2×C4×Dic9C2211yescharacteristic
53C2×C4×Dic9C2211yescharacteristic
54#63460C2218yescomplemented
55#63460C2218yescomplemented
56#63458C2218yescomplemented
57#63450C2218yescomplemented
58#63449C2218yescomplemented
59#63449C2218yescomplemented
60#63447C2218yes—
61#63447C2218yes—
62#611⋊C4C2218yes—
63#63441C2218yescomplemented
64#63440C2218yescomplemented
65#63439C2218yescomplemented
66#63434C2218yescomplemented
67C4×Dic18C2218yescomplemented
68C2×C3×#126D311yescharacteristic
69#5702—316no—
70C2×#898—31no—
71C2×#898—31no—
72C2×#896—31no—
73C2×#888—31no—
74C2×#887—31no—
75C2×#887—31no—
76C2×#885—31no—
77C2×#885—31no—
78C2×#67⋊C4—31no—
79C2×#879—31no—
80C2×#878—31no—
81C2×#877—31no—
82C2×#872—31no—
83C2×C4×Dic6—31no—
84C24×C9C2311yescharacteristic
85C23×D9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C2×#611—24no—
93C2×#611C2314yes—
94C22×Dic9—24no—
95C22×Dic9C2311yescharacteristic
96C22×Dic9C2311yescharacteristic
97C22×Dic9C2311yescharacteristic
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2314yes—
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C2×C4×D9—24no—
104C2×C4×D9C2314yes—
105C2×Dic18—24no—
106C2×Dic18—24no—
107C2×Dic18—24no—
108C2×Dic18C2314yes—
109C2×Dic18C2314yes—
110C2×Dic18C2314yes—
111C9×C4⋊C4C2314yes—
112C9×C4⋊C4C2314yes—
113C9×C4⋊C4C2314yes—
114C9×C22⋊C4C2314yes—
115C9×C22⋊C4C2314yes—
116C9×C22⋊C4C2314yes—
117C42×C9C2314yes—
118#3676C2314yes—
119#3676C2314yes—
120(C2×D9)⋊C4C2314yes—
121(C2×D9)⋊C4C2314yes—
122(C2×D9)⋊C4C2314yes—
123(C2×D9)⋊C4C2314yes—
124(C2×D9)⋊C4C2314yes—
125C4⋊Dic9C2314yes—
126C4⋊Dic9C2314yes—
127Dic9⋊C4C2314yes—
128Dic9⋊C4C2314yes—
129Dic9⋊C4C2314yes—
130Dic9⋊C4C2314yes—
131Dic9⋊C4C2314yes—
132Dic9⋊C4C2314yes—
133Dic9⋊C4C2314yes—
134C4×Dic9C2314yes—
135C4×Dic9C2314yes—
136C4×Dic9C2314yes—
137C4×Dic9C2314yes—
138C4×Dic9C2314yes—
139C4×Dic9C2314yes—
140C2×#556—91noSylow
141C22×#67—31no—
142C23×Dic3—31no—
143C22×C4×D3—31no—
144C22×Dic6—31no—
145C22×Dic6—31no—
146C22×Dic6—31no—
147C3×#126C2×D318yes—
148C2×C3×C4⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C2×D311yescharacteristic
152C2×C3×C22⋊C4C2×D311yescharacteristic
153C2×C3×C22⋊C4C2×D311yescharacteristic
154C2×C3×C42C2×D311yescharacteristic
155C2×#217—31no—
156C2×#217—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177#898—38no—
178#898—38no—
179#896—38no—
180#888—38no—
181#887—38no—
182#887—38no—
183#885—38no—
184#885—38no—
185#67⋊C4—38no—
186#879—38no—
187#878—38no—
188#877—38no—
189#872—38no—
190C4×Dic6—38no—
191C23×C9—22no—
192C23×C9—22no—
193C23×C9—22no—
194C23×C9C2412yes—
195C23×C9C2411yescharacteristic
196C22×D9—22no—
197C22×D9—22no—
198C22×D9—22no—
199C22×D9C2412yes—
200C2×C4×C9—22no—
201C2×C4×C9—22no—
202C2×C4×C9—22no—
203C2×C4×C9—22no—
204C2×C4×C9—22no—
205C2×C4×C9—22no—
206C2×C4×C9C2412yes—
207C2×C4×C9C2412yes—
208C2×C4×C9C2412yes—
209C2×C4×C9C2412yes—
210C2×C4×C9C2412yes—
211C2×C4×C9C2412yes—
212#611—28no—
213C2×Dic9—22no—
214C2×Dic9—22no—
215C2×Dic9—22no—
216C2×Dic9—22no—
217C2×Dic9—22no—
218C2×Dic9—28no—
219C2×Dic9#4114yes—
220C2×Dic9#4114yes—
221C2×Dic9C2412yes—
222C2×Dic9C2412yes—
223C2×Dic9C2412yes—
224C2×Dic9C2412yes—
225C2×Dic9C2412yes—
226C2×Dic9C2412yes—
227C2×Dic9C2412yes—
228C4×D9—28no—
229Dic18—28no—
230Dic18—28no—
231Dic18—28no—
232#556—916no—
233C2×C4⋊Q8—91no—
234C2×#126—91no—
235C2×#126—91no—
236C2×#126—91no—
237C2×#126D911yescharacteristic, complemented
238C2×#124—91no—
239C2×#124—91no—
240C2×C22⋊Q8—91no—
241C2×C22⋊Q8—91no—
242C2×C4×Q8—91no—
243C2×C4×Q8—91no—
244C2×C4×Q8—91no—
245C2×C4×D4—91no—
246C2×#117—91no—
247C2×#117—91no—
248C24×C3C22×D311yescharacteristic
249C23×D3—31no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—34no—
257C2×#67—64no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—34no—
261C22×Dic3—31no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—64no—
267C2×C4×D3—34no—
268C2×C4×D3—64no—
269C2×Dic6—34no—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—64no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C3×C4⋊C4C22×D314yes—
276C3×C4⋊C4C22×D314yes—
277C3×C4⋊C4C22×D314yes—
278C3×C22⋊C4C22×D314yes—
279C3×C22⋊C4C22×D314yes—
280C3×C22⋊C4C22×D314yes—
281C3×C42C22×D314yes—
282#217—34no—
283#217—34no—
284(C2×D3)⋊C4—34no—
285(C2×D3)⋊C4—34no—
286(C2×D3)⋊C4—34no—
287(C2×D3)⋊C4—34no—
288(C2×D3)⋊C4—34no—
289C4⋊Dic3—34no—
290C4⋊Dic3—34no—
291Dic3⋊C4—34no—
292Dic3⋊C4—34no—
293Dic3⋊C4—34no—
294Dic3⋊C4—34no—
295Dic3⋊C4—34no—
296Dic3⋊C4—34no—
297Dic3⋊C4—34no—
298C4×Dic3—34no—
299C4×Dic3—34no—
300C4×Dic3—34no—
301C4×Dic3—34no—
302C4×Dic3—34no—
303C4×Dic3—34no—
304C22×C9—22no—
305C22×C9—22no—
306C22×C9—22no—
307C22×C9—44no—
308C22×C9C2×#4112yes—
309C22×C9C2×#4112yes—
310C22×C92−1+412yes—
311C22×C9C2511yescharacteristic
312C2×D9—22no—
313C2×D9—22no—
314C2×D9—22no—
315C2×D9—44no—
316C4×C9—22no—
317C4×C9—22no—
318C4×C9—22no—
319C4×C9—22no—
320C4×C9—22no—
321C4×C9—22no—
322Dic9—22no—
323Dic9—22no—
324Dic9—22no—
325Dic9—22no—
326Dic9—22no—
327Dic9C2×#4114yes—
328Dic9C2×#4114yes—
329C22×Q8—91no—
330C22×Q8—91no—
331C22×Q8—91no—
332C22×D4—91no—
333C23×C4—91no—
334C23×C4—91no—
335C4⋊Q8—98no—
336#126—98no—
337#126—98no—
338#126—98no—
339#126C2×D918yescomplemented
340#124—98no—
341#124—98no—
342C22⋊Q8—98no—
343C22⋊Q8—98no—
344C4×Q8—98no—
345C4×Q8—98no—
346C4×Q8—98no—
347C4×D4—98no—
348#117—98no—
349#117—98no—
350C2×C4⋊C4—91no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—91no—
358C2×C4⋊C4—91no—
359C2×C4⋊C4C2×D911yescharacteristic
360C2×C4⋊C4C2×D911yescharacteristic
361C2×C4⋊C4C2×D911yescharacteristic
362C2×C22⋊C4—91no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—91no—
367C2×C22⋊C4—91no—
368C2×C22⋊C4—91no—
369C2×C22⋊C4C2×D911yescharacteristic
370C2×C22⋊C4C2×D911yescharacteristic
371C2×C22⋊C4C2×D911yescharacteristic
372C2×C42—91no—
373C2×C42—91no—
374C2×C42—91no—
375C2×C42—91no—
376C2×C42—91no—
377C2×C42—91no—
378C2×C42C2×D911yescharacteristic
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3C23×D312yes—
383C23×C3C23×D311yescharacteristic
384C22×D3—32no—
385C22×D3—62no—
386C22×D3—62no—
387C22×D3—62no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4C23×D312yes—
395C2×C3×C4C23×D312yes—
396C2×C3×C4C23×D312yes—
397C2×C3×C4C23×D312yes—
398C2×C3×C4C23×D312yes—
399C2×C3×C4C23×D312yes—
400#67—68no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—32no—
410C2×Dic3—68no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C4×D3—68no—
417Dic6—68no—
418Dic6—68no—
419Dic6—68no—
420C2×C9—42no—
421C2×C9#55614yescomplemented
422C2×C9C22×#4111yescharacteristic
423C2×C9C22×#4111yescharacteristic
424C2×C9C2×2−1+411yescharacteristic
425D9—42no—
426C24—91no—
427C24C22×D911yescharacteristic
428C2×Q8—94no—
429C2×Q8—94no—
430C2×Q8—94no—
431C2×Q8—184no—
432C2×Q8—184no—
433C2×Q8—184no—
434C2×D4—94no—
435C2×D4—184no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—94no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—94no—
445C22×C4—184no—
446C22×C4—184no—
447C22×C4C22×D911yescharacteristic
448C22×C4C22×D911yescharacteristic
449C22×C4C22×D911yescharacteristic
450C22×C4C22×D911yescharacteristic
451C22×C4C22×D911yescharacteristic
452C22×C4C22×D911yescharacteristic
453C4⋊C4—94no—
454C4⋊C4—94no—
455C4⋊C4—94no—
456C4⋊C4—94no—
457C4⋊C4—94no—
458C4⋊C4—94no—
459C4⋊C4—94no—
460C4⋊C4—94no—
461C4⋊C4—94no—
462C4⋊C4C22×D914yes—
463C4⋊C4C22×D914yes—
464C4⋊C4C22×D914yes—
465C22⋊C4—94no—
466C22⋊C4—94no—
467C22⋊C4—94no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—94no—
472C22⋊C4C22×D914yes—
473C22⋊C4C22×D914yes—
474C22⋊C4C22×D914yes—
475C42—94no—
476C42—94no—
477C42—94no—
478C42—94no—
479C42—94no—
480C42—94no—
481C42C22×D914yes—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—44no—
486C22×C3D3×#4112yes—
487C22×C3D3×#4112yes—
488C22×C3#101012yes—
489C22×C3C24×D311yescharacteristic
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—124no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—22no—
498C3×C4—22no—
499C3×C4—22no—
500Dic3—34no—
501Dic3—34no—
502Dic3—62no—
503Dic3—62no—
504Dic3—62no—
505Dic3—62no—
506Dic3—62no—
507C9C2×#55611yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—92no—
512C23—182no—
513C23—182no—
514C23—182no—
515C23C23×D912yes—
516C23C23×D911yescharacteristic
517Q8—188no—
518Q8—188no—
519Q8—188no—
520D4—188no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—92no—
528C2×C4—92no—
529C2×C4—94no—
530C2×C4—94no—
531C2×C4—92no—
532C2×C4—92no—
533C2×C4—92no—
534C2×C4—92no—
535C2×C4—92no—
536C2×C4—188no—
537C2×C4—188no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4C23×D912yes—
544C2×C4C23×D912yes—
545C2×C4C23×D912yes—
546C2×C4C23×D912yes—
547C2×C4C23×D912yes—
548C2×C4C23×D912yes—
549C2×C3—42no—
550C2×C3#570214yes—
551C2×C3C2×D3×#4111yescharacteristic
552C2×C3C2×D3×#4111yescharacteristic
553C2×C3C2×#101011yescharacteristic
554D3—122no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—44no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—364no—
563C22#41×D912yes—
564C22#41×D912yes—
565C22#6371612yes—
566C22C24×D911yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—94no—
574C4—94no—
575C4—182no—
576C4—182no—
577C4—182no—
578C4—182no—
579C4—182no—
580C3C2×#570211yescharacteristic
581C2—42no—
582C2—362no—
583C2#1058980414yesdirect product factor
584C2C2×#41×D911yescharacteristic
585C2C2×#41×D911yescharacteristic
586C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#126C2
socleC23×C3C23×D3
prime radicalC22×#611C22
hypercenterC2×#126D9
hypocenterC9C2×#556
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×C9×#126C2semidirect
2. #10589804C2direct (N × H)
3. C2×#63460C2semidirect
4. C2×#63460C2semidirect
5. C2×#63458C2semidirect
6. C2×#63450C2semidirect
7. C2×#63449C2semidirect
8. C2×#63449C2semidirect
12. C2×#63441C2semidirect
13. C2×#63440C2semidirect
14. C2×#63439C2semidirect
15. C2×#63434C2semidirect
16. C2×C4×Dic18C2semidirect
24. C9×#126C22semidirect
54. #63460C22semidirect
55. #63460C22semidirect
56. #63458C22semidirect
57. #63450C22semidirect
58. #63449C22semidirect
59. #63449C22semidirect
63. #63441C22semidirect
64. #63440C22semidirect
65. #63439C22semidirect
66. #63434C22semidirect
67. C4×Dic18C22semidirect
237. C2×#126D9semidirect
339. #126C2×D9semidirect
421. C2×C9#556semidirect
507. C9C2×#556semidirect
583. C2#10589804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1262
#105898042
C2×#634602
C2×#634582
C2×#634502
C2×#634492
C2×#634472
C2×#611⋊C42
C2×#634412
C2×#634402
C2×#634392
C2×#634342
C2×C4×Dic182
C2×#57023