Finite Group Databasebeta

← #11805480

Subgroups — #11805480

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#611C211yesmaximal, characteristic
2C2×#611⋊C4C211yesmaximal, characteristic
3C2×#611⋊C4C211yesmaximal, characteristic
4C9×#385C211yesmaximal, characteristic, complemented
5C2×C9⋊#95C211yesmaximal, characteristic, complemented
6#10588669C211yesmaximal, characteristic, complemented
7#10588667C211yesmaximal, characteristic, complemented
8#10588656C211yesmaximal, characteristic, complemented
9C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
10#10588630C211yesmaximal, characteristic, complemented
11#10588622C211yesmaximal, characteristic, complemented
12#10588348C211yesmaximal, characteristic, complemented
13D9×#95C211yesmaximal, characteristic, complemented
14#10588330C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#74394—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C22×#611C2211yescharacteristic
19C23×Dic9C2211yescharacteristic
20C23×Dic9C2211yescharacteristic
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C4⋊C4C2211yescharacteristic
26C2×C9×C22⋊C4C2211yescharacteristic
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29C4×#611—24no—
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
32C2×(C2×D9)⋊C4C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43#611⋊C4—24no—
44#611⋊C4C418yescomplemented
45C9×#95C2211yescharacteristic
46C9×#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×C4×#67—31no—
56C2×#67⋊C4—31no—
57C2×#67⋊C4—31no—
58C3×#385D311yescharacteristic
59C2×C3⋊#95—31no—
60#4989—31no—
61#4987—31no—
62#4976—31no—
63Dic3×C4⋊C4—31no—
64#4950—31no—
65#4942—31no—
66#4668—31no—
67D3×#95—31no—
68#4650—31no—
69#4647—31no—
70C24×C9C2311yescharacteristic
71C23×D9C2311yescharacteristic
72C22×C4×C9—22no—
73C22×C4×C9—22no—
74C22×C4×C9—41no—
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C2×#611C2×C414yes—
82C2×#611D414yes—
83C2×#611Q814yes—
84C22×Dic9—22no—
85C22×Dic9—22no—
86C22×Dic9—41no—
87C22×Dic9—41no—
88C22×Dic9—41no—
89C22×Dic9C2×C414yescomplemented
90C22×Dic9C2311yescharacteristic
91C22×Dic9C2311yescharacteristic
92C22×Dic9C2311yescharacteristic
93C22×Dic9C2311yescharacteristic
94C22×Dic9C2311yescharacteristic
95C22×Dic9C2311yescharacteristic
96C22×Dic9C2311yescharacteristic
97C2×C4×D9—22no—
98C2×C4×D9—22no—
99C2×C4×D9—22no—
100C2×C4×D9—22no—
101C2×C4×D9—41no—
102C2×C4×D9—41no—
103C2×C4×D9—41no—
104C2×C4×D9—41no—
105C2×C4×D9C2×C414yescomplemented
106C9×C4⋊C4—22no—
107C9×C4⋊C4—41no—
108C9×C22⋊C4—22no—
109C9×C22⋊C4C2×C414yescomplemented
110#3676—22no—
111(C2×D9)⋊C4—22no—
112(C2×D9)⋊C4—22no—
113(C2×D9)⋊C4C2×C414yescomplemented
114C4⋊Dic9—22no—
115C4⋊Dic9—41no—
116Dic9⋊C4—22no—
117Dic9⋊C4—22no—
118Dic9⋊C4—41no—
119Dic9⋊C4—41no—
120Dic9⋊C4C2×C414yescomplemented
121C4×Dic9—22no—
122C4×Dic9—22no—
123C4×Dic9C2×C414yescomplemented
124#2349—91noSylow
125C23×C3×C4C2×D311yescharacteristic
126C22×#67—31no—
127C23×Dic3—31no—
128C23×Dic3—31no—
129C22×C4×D3—31no—
130C22×C4×D3—31no—
131C22×C4×D3—31no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C2×D311yescharacteristic
136C2×#217—31no—
137C4×#67—64no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×C4×Dic3—31no—
149C2×C4×Dic3—31no—
150C2×C4×Dic3—31no—
151#67⋊C4—38no—
152#67⋊C4—64no—
153C3×#95C2×D311yescharacteristic
154C3×#95C2×D311yescharacteristic
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—31no—
162C3⋊#95—31no—
163C23×C9—21no—
164C23×C9—21no—
165C23×C9—21no—
166C23×C9—21no—
167C23×C9C22×C412yes—
168C23×C9C2×D412yes—
169C23×C9C2×Q812yes—
170C23×C9C2411yescharacteristic
171C22×D9—21no—
172C22×D9—21no—
173C22×D9—21no—
174C22×D9—21no—
175C22×D9C22×C412yes—
176C22×D9C2×D412yes—
177C22×D9C2×Q812yes—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—21no—
191C2×C4×C9—21no—
192C2×C4×C9—21no—
193C2×C4×C9—44no—
194C2×C4×C9C22×C412yes—
195C2×C4×C9C22×C412yes—
196C2×C4×C9#4112yes—
197#611C4⋊C4116yescomplemented
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—21no—
202C2×Dic9—21no—
203C2×Dic9—21no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9—21no—
207C2×Dic9—21no—
208C2×Dic9—21no—
209C2×Dic9—21no—
210C2×Dic9—21no—
211C2×Dic9—21no—
212C2×Dic9—21no—
213C2×Dic9—44no—
214C2×Dic9—44no—
215C2×Dic9C22×C412yes—
216C2×Dic9C22×C412yes—
217C2×Dic9C22×C412yes—
218C2×Dic9C2×D412yes—
219C2×Dic9C2×Q812yes—
220C2×Dic9#4112yes—
221C4×D9—44no—
222C4×D9—44no—
223C4×D9—44no—
224C2×C4×D4—91no—
225C2×C4×D4—91no—
226C2×C4×D4—91no—
227#389—91no—
228#389—91no—
229#385—91no—
230#385—91no—
231#385—91no—
232#385D911yescharacteristic, complemented
233#382—91no—
234#380—91no—
235#380—91no—
236C4×C4⋊C4—91no—
237C2×#95—91no—
238C2×#95—91no—
239C24×C3C22×D311yescharacteristic
240C23×D3—31no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—41no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—34no—
251C2×#67—34no—
252C2×#67—34no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—34no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—31no—
261C22×Dic3—62no—
262C22×Dic3—62no—
263C22×Dic3—121no—
264C22×Dic3—121no—
265C22×Dic3—121no—
266C2×C4×D3—34no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—62no—
271C2×C4×D3—121no—
272C2×C4×D3—121no—
273C2×C4×D3—121no—
274C2×C4×D3—121no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—41no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4C4×D314yes—
279#217—62no—
280(C2×D3)⋊C4—34no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—121no—
285Dic3⋊C4—34no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—121no—
289Dic3⋊C4—121no—
290C4×Dic3—34no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C22×C9—22no—
294C22×C9—22no—
295C22×C9—22no—
296C22×C9—22no—
297C22×C9—22no—
298C22×C9—22no—
299C22×C9C2×C4⋊C414yes—
300C22×C9C23×C411yescharacteristic
301C22×C9C22×D411yescharacteristic
302C22×C9C22×Q811yescharacteristic
303C22×C9C2×#4111yescharacteristic
304C22×C9C2×#4111yescharacteristic
305C22×C9H(5,𝔽2)11yescharacteristic
306C22×C9H(5,𝔽2)11yescharacteristic
307C2×D9—22no—
308C2×D9—22no—
309C2×D9—22no—
310C2×D9—22no—
311C2×D9—22no—
312C2×D9—22no—
313C2×D9C2×C4⋊C414yes—
314C4×C9—22no—
315C4×C9—22no—
316C4×C9—22no—
317C4×C9—41no—
318C4×C9—41no—
319C4×C9—41no—
320Dic9—22no—
321Dic9—22no—
322Dic9—22no—
323Dic9—41no—
324Dic9—41no—
325Dic9—41no—
326Dic9C2×C4⋊C414yes—
327C22×D4—91no—
328C23×C4—91no—
329C23×C4—91no—
330C23×C4—91no—
331C23×C4—91no—
332C23×C4—91no—
333C23×C4C2×D911yescharacteristic
334C4×D4—98no—
335C4×D4—184no—
336C4×D4—184no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—91no—
339C2×C4⋊C4—91no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C4⋊C4C2×D911yescharacteristic
345C2×C4⋊C4C2×D911yescharacteristic
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4C2×D911yescharacteristic
351C2×C22⋊C4C2×D911yescharacteristic
352C2×C42—91no—
353C2×C42—91no—
354C2×C42—91no—
355#95—91no—
356#95—91no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362#95—91no—
363#95C2×D911yescharacteristic
364#95C2×D911yescharacteristic
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3C2×C4×D312yes—
370C23×C3D3×D412yes—
371C23×C3D3×Q812yes—
372C23×C3C23×D311yescharacteristic
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—32no—
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—44no—
396C2×C3×C4C2×C4×D312yes—
397C2×C3×C4C2×C4×D312yes—
398C2×C3×C4#23712yes—
399#67—316no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—124no—
422C2×Dic3—124no—
423C4×D3—124no—
424C4×D3—124no—
425C4×D3—124no—
426C2×C9—24no—
427C2×C9C22×C4⋊C411yescharacteristic
428C2×C9C4×#4111yescharacteristic
429C2×C9#51811yescharacteristic
430C2×C9#54611yescharacteristic
431C2×C9#54611yescharacteristic
432C2×C9#55411yescharacteristic
433C2×C9#55411yescharacteristic
434D9—24no—
435C24—91no—
436C24C22×D911yescharacteristic
437C2×D4—94no—
438C2×D4—94no—
439C2×D4—94no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—91no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—94no—
448C22×C4—94no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—182no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4—182no—
457C22×C4—182no—
458C22×C4—361no—
459C22×C4—361no—
460C22×C4—361no—
461C22×C4—361no—
462C22×C4—361no—
463C22×C4—361no—
464C22×C4—361no—
465C22×C4C22×D911yescharacteristic
466C22×C4C22×D911yescharacteristic
467C22×C4C22×D911yescharacteristic
468C22×C4C22×D911yescharacteristic
469C22×C4C22×D911yescharacteristic
470C22×C4C22×D911yescharacteristic
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—94no—
474C4⋊C4—182no—
475C4⋊C4—182no—
476C4⋊C4—182no—
477C4⋊C4—361no—
478C4⋊C4—361no—
479C4⋊C4—361no—
480C22⋊C4—22no—
481C22⋊C4—94no—
482C22⋊C4—182no—
483C22⋊C4—182no—
484C22⋊C4—182no—
485C22⋊C4C4×D914yescomplemented
486C42—94no—
487C42—182no—
488C42—182no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3D3×C4⋊C414yes—
496C22×C3C22×C4×D311yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×#23711yescharacteristic
499C22×C3#100411yescharacteristic
500C22×C3C2×D3×Q811yescharacteristic
501C22×C3D3×#4111yescharacteristic
502C22×C3#100911yescharacteristic
503C2×D3—34no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—41no—
516Dic3—34no—
517Dic3—62no—
518Dic3—62no—
519Dic3—62no—
520Dic3—121no—
521Dic3—121no—
522Dic3—121no—
523C9#234911yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—92no—
529C23—92no—
530C23—92no—
531C23—181no—
532C23—181no—
533C23—181no—
534C23—181no—
535C23C2×C4×D912yes—
536C23D4×D912yes—
537C23Q8×D912yes—
538C23C23×D911yescharacteristic
539D4—916no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—44no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—181no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—364no—
578C2×C4—364no—
579C2×C4—364no—
580C2×C4—364no—
581C2×C4—364no—
582C2×C4C2×C4×D912yes—
583C2×C4C2×C4×D912yes—
584C2×C4#369912yes—
585C2×C3—24no—
586C2×C3C2×D3×C4⋊C411yescharacteristic
587C2×C3C4×#23711yescharacteristic
588C2×C3#554511yescharacteristic
589C2×C3#559111yescharacteristic
590C2×C3#563511yescharacteristic
591C2×C3#563611yescharacteristic
592C2×C3#565411yescharacteristic
593D3—64no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—94no—
601C22—182no—
602C22—182no—
603C22—182no—
604C22—182no—
605C22—182no—
606C22—182no—
607C22C4⋊C4×D914yes—
608C22C22×C4×D911yescharacteristic
609C22C2×D4×D911yescharacteristic
610C22C2×#369911yescharacteristic
611C22#6371011yescharacteristic
612C22C2×Q8×D911yescharacteristic
613C22#41×D911yescharacteristic
614C22#6371511yescharacteristic
615C4—22no—
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—94no—
622C4—182no—
623C4—182no—
624C4—182no—
625C4—361no—
626C4—361no—
627C4—361no—
628C3#7439411yescharacteristic
629C2—24no—
630C2—184no—
631C2C2×C4⋊C4×D911yescharacteristic
632C2C4×#369911yescharacteristic
633C2#1058964711yescharacteristic
634C2#1058969311yescharacteristic
635C2#1058973711yescharacteristic
636C2#1058973811yescharacteristic
637C2#1058975611yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#385C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenter#385D9
hypocenterC9#2349
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. C9×#385C2semidirect
5. C2×C9⋊#95C2semidirect
6. #10588669C2semidirect
7. #10588667C2semidirect
8. #10588656C2semidirect
9. C4⋊C4×Dic9C2semidirect
10. #10588630C2semidirect
11. #10588622C2semidirect
12. #10588348C2semidirect
13. D9×#95C2semidirect
14. #10588330C2semidirect
15. #10588327C2semidirect
44. #611⋊C4C4semidirect
89. C22×Dic9C2×C4semidirect
105. C2×C4×D9C2×C4semidirect
109. C9×C22⋊C4C2×C4semidirect
113. (C2×D9)⋊C4C2×C4semidirect
120. Dic9⋊C4C2×C4semidirect
123. C4×Dic9C2×C4semidirect
197. #611C4⋊C4semidirect
232. #385D9semidirect
485. C22⋊C4C4×D9semidirect
523. C9#2349semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C2×#611⋊C42
C9×#3852
C2×C9⋊#952
#105886692
#105886672
#105886562
C4⋊C4×Dic92
#105886302
#105886222
#105883482
D9×#952
#105883302
#105883272
#743943