Finite Group Databasebeta

← #11817712

Subgroups — #11817712

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63460C211yesmaximal, characteristic, complemented
2C2×#63454C211yesmaximal, characteristic, complemented
3C9×#387C211yesmaximal, characteristic, complemented
4#10588671C211yesmaximal, characteristic
5#10588664C211yesmaximal, characteristic, complemented
6#10588619C211yesmaximal, characteristic
7C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
8#10588357C211yesmaximal, characteristic, complemented
9#10588357C211yesmaximal, characteristic, complemented
10#10588350C211yesmaximal, characteristic, complemented
11#10588350C211yesmaximal, characteristic, complemented
12#10588350C211yesmaximal, characteristic, complemented
13#10588348C211yesmaximal, characteristic, complemented
14#10588345C211yesmaximal, characteristic
15#10588341C211yesmaximal, characteristic, complemented
16#75018—31nomaximal
17C22×D36C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C42×C9C2211yescharacteristic
22C2×(C2×D9)⋊C4C2211yescharacteristic
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2211yescharacteristic
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
32C2×(C2×D9)⋊C4C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×C4⋊Dic9C2211yescharacteristic
37C2×C4⋊Dic9C2211yescharacteristic
38C2×C4⋊Dic9C2211yescharacteristic
39C2×C4⋊Dic9C2211yescharacteristic
40C2×Dic9⋊C4C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43C2×C4×Dic9C2211yescharacteristic
44#63460—24no—
45#63454—24no—
46C9×#95C2211yescharacteristic
47C9×#95C2211yescharacteristic
48C9×#95C2211yescharacteristic
49C9×#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C2×#898—31no—
55C2×#892—31no—
56C3×#387D311yescharacteristic
57#4991—31no—
58#4984—31no—
59#4939—31no—
60C4×C4⋊Dic3—31no—
61#4677—31no—
62#4677—31no—
63#4670—31no—
64#4670—31no—
65#4670—31no—
66#4668—31no—
67#4665—31no—
68#4661—31no—
69C23×D9C2311yescharacteristic
70C23×D9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C2×D36—22no—
85C2×D36—22no—
86C2×D36—41no—
87C2×C4×D9—22no—
88C2×C4×D9—22no—
89C2×C4×D9—22no—
90C9×C4⋊C4—22no—
91C9×C4⋊C4D414yescomplemented
92C42×C9—22no—
93(C2×D9)⋊C4—22no—
94(C2×D9)⋊C4—22no—
95(C2×D9)⋊C4—22no—
96(C2×D9)⋊C4—22no—
97(C2×D9)⋊C4—22no—
98(C2×D9)⋊C4—22no—
99(C2×D9)⋊C4—22no—
100(C2×D9)⋊C4—22no—
101(C2×D9)⋊C4—22no—
102(C2×D9)⋊C4—41no—
103(C2×D9)⋊C4—41no—
104C4⋊Dic9—22no—
105C4⋊Dic9—22no—
106C4⋊Dic9—22no—
107C4⋊Dic9—22no—
108C4⋊Dic9—41no—
109C4⋊Dic9—41no—
110C4⋊Dic9—41no—
111Dic9⋊C4—22no—
112C4×Dic9—22no—
113C4×Dic9—22no—
114C4×Dic9—22no—
115#2479—91noSylow
116C22×D12—31no—
117C22×C4×D3—31no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C42C2×D311yescharacteristic
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×Dic3⋊C4—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—31no—
143#898—64no—
144#892—64no—
145C3×#95C2×D311yescharacteristic
146C3×#95C2×D311yescharacteristic
147C3×#95C2×D311yescharacteristic
148C3×#95C2×D311yescharacteristic
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C23×C9C2411yescharacteristic
154C22×D9—21no—
155C22×D9—21no—
156C22×D9—21no—
157C22×D9—21no—
158C22×D9—21no—
159C22×D9—21no—
160C22×D9—21no—
161C22×D9—21no—
162C22×D9—21no—
163C22×D9—21no—
164C22×D9—21no—
165C22×D9—21no—
166C22×D9—21no—
167C22×D9#4112yes—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
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×C9C2×D412yes—
185C2×C4×C9C2×D412yes—
186C2×C4×C9C2×D412yes—
187C2×C4×C9#4112yes—
188C2×C4×C9#4112yes—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—21no—
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#4112yes—
207D36—44no—
208C4×D9—28no—
209C2×#126—91no—
210C2×#117—91no—
211#399—91no—
212#399—91no—
213#398—91no—
214#394—91no—
215#390—91no—
216#389—91no—
217#388—91no—
218#388—91no—
219#388—91no—
220#387D911yescharacteristic, complemented
221#386—91no—
222#385—91no—
223C4×C4⋊C4—91no—
224C23×D3—31no—
225C23×D3—31no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C2×D12—62no—
240C2×D12—62no—
241C2×D12—121no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4D1214yes—
247C3×C42—22no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—121no—
258(C2×D3)⋊C4—121no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—121no—
264C4⋊Dic3—121no—
265C4⋊Dic3—121no—
266Dic3⋊C4—62no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C22×C9C22×D411yescharacteristic
271C22×C9C2×#4111yescharacteristic
272C22×C9C2×#4111yescharacteristic
273C22×C9C2×#4111yescharacteristic
274C22×C9C2×#4111yescharacteristic
275C22×C9H(5,𝔽2)11yescharacteristic
276C22×C92−1+411yescharacteristic
277C2×D9—22no—
278C2×D9—22no—
279C2×D9—22no—
280C2×D9—41no—
281C2×D9—41no—
282C2×D9—41no—
283C2×D9—41no—
284C2×D9—41no—
285C2×D9—41no—
286C2×D9—41no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C4×C9—22no—
292C4×C9—22no—
293C4×C9—22no—
294C4×C9—22no—
295C4×C9—22no—
296C4×C9—41no—
297C4×C9—41no—
298Dic9—22no—
299Dic9—41no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304C22×D4—91no—
305C23×C4—91no—
306#126—184no—
307#117—184no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4C2×D911yescharacteristic
317C2×C4⋊C4C2×D911yescharacteristic
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—91no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C42—91no—
330C2×C42—91no—
331C2×C42—91no—
332C2×C42C2×D911yescharacteristic
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95C2×D911yescharacteristic
338#95C2×D911yescharacteristic
339#95C2×D911yescharacteristic
340#95C2×D911yescharacteristic
341C23×C3C23×D311yescharacteristic
342C22×D3—32no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4C2×D1212yes—
373C2×C3×C4C2×D1212yes—
374C2×C3×C4C2×D1212yes—
375C2×C3×C4#23712yes—
376C2×C3×C4#23912yes—
377C2×Dic3—32no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395D12—124no—
396C4×D3—68no—
397C2×C9#52511yescharacteristic
398C2×C9#52911yescharacteristic
399C2×C9#54211yescharacteristic
400C2×C9#54711yescharacteristic
401C2×C9#55011yescharacteristic
402C2×C9#55111yescharacteristic
403C2×C9#55211yescharacteristic
404D9—42no—
405D9—81no—
406C24—91no—
407C24—91no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—361no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4C22×D911yescharacteristic
421C22×C4C22×D911yescharacteristic
422C22×C4C22×D911yescharacteristic
423C22×C4C22×D911yescharacteristic
424C22×C4C22×D911yescharacteristic
425C22×C4C22×D911yescharacteristic
426C22×C4C22×D911yescharacteristic
427C4⋊C4—22no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—361no—
434C4⋊C4—361no—
435C4⋊C4—361no—
436C4⋊C4D3614yescomplemented
437C22⋊C4—182no—
438C22⋊C4—182no—
439C22⋊C4—182no—
440C22⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—182no—
443C22⋊C4—182no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—361no—
447C22⋊C4—361no—
448C42—22no—
449C42—182no—
450C42—182no—
451C42—182no—
452C22×C3C22×D1211yescharacteristic
453C22×C3C2×#23711yescharacteristic
454C22×C3C2×#23911yescharacteristic
455C22×C3D3×#4111yescharacteristic
456C22×C3D3×#4111yescharacteristic
457C22×C3#100911yescharacteristic
458C22×C3#101011yescharacteristic
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—41no—
479C3×C4—41no—
480Dic3—62no—
481Dic3—121no—
482Dic3—121no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486C9#247911yescharacteristic, complemented, Sylow
487C23—92no—
488C23—181no—
489C23—181no—
490C23—181no—
491C23—181no—
492C23—181no—
493C23—181no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23C23×D911yescharacteristic
502D4—364no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—92no—
520C2×C4—188no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4C2×D3612yes—
539C2×C4C2×D3612yes—
540C2×C4C2×D3612yes—
541C2×C4#369912yes—
542C2×C4#370112yes—
543C2×C3#552411yescharacteristic
544C2×C3#555511yescharacteristic
545C2×C3#557711yescharacteristic
546C2×C3#562411yescharacteristic
547C2×C3#565811yescharacteristic
548C2×C3#569411yescharacteristic
549C2×C3#571011yescharacteristic
550D3—122no—
551D3—241no—
552C22—182no—
553C22—182no—
554C22—182no—
555C22—361no—
556C22—361no—
557C22—361no—
558C22—361no—
559C22—361no—
560C22—361no—
561C22—361no—
562C22—361no—
563C22—361no—
564C22—361no—
565C22—361no—
566C22C22×D3611yescharacteristic
567C22C2×#369911yescharacteristic
568C22C2×#370111yescharacteristic
569C22#41×D911yescharacteristic
570C22#41×D911yescharacteristic
571C22#6371511yescharacteristic
572C22#6371611yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—182no—
581C4—361no—
582C4—361no—
583C4—361no—
584C4—361no—
585C4—361no—
586C3#7501811yescharacteristic
587C2—362no—
588C2—721no—
589C2#1058962611yescharacteristic
590C2#1058965711yescharacteristic
591C2#1058967911yescharacteristic
592C2#1058972611yescharacteristic
593C2#1058976011yescharacteristic
594C2#1058979611yescharacteristic
595C2#1058981211yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#387C2
prime radicalC22×D36C22
hypercenter#387D9
hypocenterC9#2479
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#63460C2semidirect
2. C2×#63454C2semidirect
3. C9×#387C2semidirect
5. #10588664C2semidirect
7. C4×C4⋊Dic9C2semidirect
8. #10588357C2semidirect
9. #10588357C2semidirect
10. #10588350C2semidirect
11. #10588350C2semidirect
12. #10588350C2semidirect
13. #10588348C2semidirect
15. #10588341C2semidirect
91. C9×C4⋊C4D4semidirect
220. #387D9semidirect
436. C4⋊C4D36semidirect
486. C9#2479semidirect

Maximal subgroups

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

subgroupindex
C2×#634602
C2×#634542
C9×#3872
#105886712
#105886642
#105886192
C4×C4⋊Dic92
#105883572
#105883502
#105883482
#105883452
#105883412
#750183