Finite Group Databasebeta

← #11808656

Subgroups — #11808656

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63488C211yesmaximal, characteristic
2C2×C4×Dic18C211yesmaximal, characteristic, complemented
3C4×C9×C22⋊C4C211yesmaximal, characteristic
4C4×#3676C211yesmaximal, characteristic
5#10588629C211yesmaximal, characteristic
6#10588628C211yesmaximal, characteristic
7#10588628C211yesmaximal, characteristic
8#10588627C211yesmaximal, characteristic
9C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
10C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#10588341C211yesmaximal, characteristic, complemented
13#10588340C211yesmaximal, characteristic, complemented
14#10588337C211yesmaximal, characteristic, complemented
15#10588336C211yesmaximal, characteristic, complemented
16#73480—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C22×Dic18C2211yescharacteristic
19C2×C9×C22⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4C2211yescharacteristic
21C2×C42×C9C2211yescharacteristic
22C2×C42×C9C2211yescharacteristic
23C2×#3676C2211yescharacteristic
24C2×#3676C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27#63488—24no—
28C2×C4⋊Dic9C2211yescharacteristic
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2211yescharacteristic
31C2×C4⋊Dic9C2211yescharacteristic
32C2×C4⋊Dic9C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43C4×Dic18—24no—
44C9×#95C2211yescharacteristic
45C9×#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C2×#926—31no—
55C2×C4×Dic6—31no—
56C3×C4×C22⋊C4D311yescharacteristic
57C4×#217—31no—
58#4949—31no—
59#4948—31no—
60#4948—31no—
61#4947—31no—
62C4×C4⋊Dic3—31no—
63C4×Dic3⋊C4—31no—
64C4×Dic3⋊C4—31no—
65#4661—31no—
66#4660—31no—
67#4657—31no—
68#4656—31no—
69C24×C9C2311yescharacteristic
70C22×C4×C9—22no—
71C22×C4×C9—22no—
72C22×C4×C9Q814yescomplemented
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C2×Dic18—22no—
88C2×Dic18—22no—
89C2×Dic18—22no—
90C9×C22⋊C4—22no—
91C9×C22⋊C4—22no—
92C42×C9—22no—
93C42×C9—22no—
94#3676—22no—
95#3676—22no—
96#3676—22no—
97#3676—22no—
98C4⋊Dic9—22no—
99C4⋊Dic9—22no—
100C4⋊Dic9—22no—
101C4⋊Dic9—22no—
102C4⋊Dic9—22no—
103Dic9⋊C4—22no—
104Dic9⋊C4—22no—
105Dic9⋊C4—22no—
106Dic9⋊C4—22no—
107Dic9⋊C4—22no—
108Dic9⋊C4—22no—
109C4×Dic9—22no—
110C4×Dic9—22no—
111C4×Dic9—22no—
112C4×Dic9D414yes—
113#2396—91noSylow
114C23×C3×C4C2×D311yescharacteristic
115C22×Dic6—31no—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×C3×C42C2×D311yescharacteristic
119C2×C3×C42C2×D311yescharacteristic
120C2×#217—31no—
121C2×#217—31no—
122C2×#217—31no—
123C2×#217—31no—
124#926—64no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138C2×C4×Dic3—31no—
139C2×C4×Dic3—31no—
140C4×Dic6—64no—
141C3×#95C2×D311yescharacteristic
142C3×#95C2×D311yescharacteristic
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C23×C9—21no—
152C23×C9—21no—
153C23×C9—21no—
154C23×C9—21no—
155C23×C9—21no—
156C23×C9—21no—
157C23×C9C2×Q812yes—
158C23×C9C2411yescharacteristic
159C2×C4×C9—21no—
160C2×C4×C9—21no—
161C2×C4×C9—21no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—28no—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9C2×D412yes—
173C2×C4×C9C2×Q812yes—
174C2×C4×C9C2×Q812yes—
175C2×C4×C9#4112yes—
176C2×C4×C9#4112yes—
177C2×C4×C9#4112yes—
178C2×Dic9—21no—
179C2×Dic9—21no—
180C2×Dic9—21no—
181C2×Dic9—21no—
182C2×Dic9—21no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
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×Dic9C2×D412yes—
199C2×Dic9C2×D412yes—
200C2×Dic9#4112yes—
201C2×Dic9#4112yes—
202Dic18—28no—
203C2×C4×Q8—91no—
204C2×#117—91no—
205#400—91no—
206#399—91no—
207#398—91no—
208#398—91no—
209#396—91no—
210#396—91no—
211#395—91no—
212#393—91no—
213C4×C4⋊C4—91no—
214C4×C4⋊C4—91no—
215C4×C4⋊C4—91no—
216C4×C22⋊C4—91no—
217C4×C22⋊C4D911yescharacteristic
218C24×C3C22×D311yescharacteristic
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4Dic614yes—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C2×Dic6—62no—
237C2×Dic6—62no—
238C2×Dic6—62no—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C42—22no—
242C3×C42—22no—
243#217—62no—
244#217—62no—
245#217—62no—
246#217—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258C4×Dic3—34no—
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C22×C9—22no—
263C22×C9—22no—
264C22×C9—22no—
265C22×C9—41no—
266C22×C9—41no—
267C22×C9—41no—
268C22×C9—41no—
269C22×C9C22×D411yescharacteristic
270C22×C9C22×Q811yescharacteristic
271C22×C9C2×#4111yescharacteristic
272C22×C9C2×#4111yescharacteristic
273C22×C9C2×#4111yescharacteristic
274C22×C9C2×#4111yescharacteristic
275C22×C9C2×#4111yescharacteristic
276C4×C9—22no—
277C4×C9—22no—
278C4×C9—22no—
279C4×C9—41no—
280C4×C9—41no—
281C4×C9C22⋊Q814yes—
282Dic9—22no—
283Dic9—22no—
284Dic9—22no—
285Dic9—22no—
286Dic9—41no—
287Dic9—41no—
288Dic9—41no—
289Dic9—41no—
290C22×Q8—91no—
291C23×C4C2×D911yescharacteristic
292C4×Q8—184no—
293#117—184no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C22⋊C4—91no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4C2×D911yescharacteristic
310C2×C22⋊C4C2×D911yescharacteristic
311C2×C42—91no—
312C2×C42—91no—
313C2×C42—91no—
314C2×C42—91no—
315C2×C42C2×D911yescharacteristic
316C2×C42C2×D911yescharacteristic
317#95—91no—
318#95—91no—
319#95—91no—
320#95—91no—
321#95—91no—
322#95—91no—
323#95—91no—
324#95—91no—
325#95C2×D911yescharacteristic
326#95C2×D911yescharacteristic
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3C2×Dic612yes—
334C23×C3C23×D311yescharacteristic
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—28no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4C2×Dic612yes—
349C2×C3×C4C2×Dic612yes—
350C2×C3×C4#23512yes—
351C2×C3×C4#23512yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378Dic6—68no—
379C2×C9—42no—
380C2×C9C2×C22⋊Q811yescharacteristic
381C2×C9#52511yescharacteristic
382C2×C9#52911yescharacteristic
383C2×C9#52911yescharacteristic
384C2×C9#53211yescharacteristic
385C2×C9#53311yescharacteristic
386C2×C9#53311yescharacteristic
387C24C22×D911yescharacteristic
388C2×Q8—182no—
389C2×Q8—182no—
390C2×Q8—182no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4Dic1814yescomplemented
402C22×C4C22×D911yescharacteristic
403C22×C4C22×D911yescharacteristic
404C22×C4C22×D911yescharacteristic
405C22×C4C22×D911yescharacteristic
406C22×C4C22×D911yescharacteristic
407C22×C4C22×D911yescharacteristic
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—22no—
426C42—22no—
427C42—94no—
428C42—182no—
429C42—182no—
430C42—182no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3C22×Dic611yescharacteristic
439C22×C3C2×#23511yescharacteristic
440C22×C3C2×#23511yescharacteristic
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C2×#23711yescharacteristic
443C22×C3D3×#4111yescharacteristic
444C22×C3D3×#4111yescharacteristic
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4#87814yes—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459C9#239611yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23C2×Dic1812yes—
467C23C23×D911yescharacteristic
468Q8—188no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—28no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4C2×Dic1812yes—
507C2×C4C2×Dic1812yes—
508C2×C4#369712yes—
509C2×C4#369712yes—
510C2×C4D4×D912yes—
511C2×C4#369912yes—
512C2×C3—42no—
513C2×C3#547011yescharacteristic
514C2×C3C2×#87811yescharacteristic
515C2×C3#551711yescharacteristic
516C2×C3#553811yescharacteristic
517C2×C3#554711yescharacteristic
518C2×C3#554811yescharacteristic
519C2×C3#555711yescharacteristic
520C22—22no—
521C22—22no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22C22×Dic1811yescharacteristic
528C22C2×#369711yescharacteristic
529C22C2×#369711yescharacteristic
530C22C2×D4×D911yescharacteristic
531C22C2×#369911yescharacteristic
532C22#41×D911yescharacteristic
533C22#41×D911yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—182no—
540C4—182no—
541C4—182no—
542C4—182no—
543C4—361no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4#6344014yes—
548C3#7348011yescharacteristic
549C2—42no—
550C2#1058957211yescharacteristic
551C2C2×#6344011yescharacteristic
552C2#1058961911yescharacteristic
553C2#1058964011yescharacteristic
554C2#1058964911yescharacteristic
555C2#1058965011yescharacteristic
556C2#1058965911yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC4×C9×C22⋊C4C2
prime radicalC24×C3C22×D3
hypercenterC4×C22⋊C4D9
hypocenterC9#2396
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic18C2semidirect
9. C4×C4⋊Dic9C2semidirect
10. C4×Dic9⋊C4C2semidirect
11. C4×Dic9⋊C4C2semidirect
12. #10588341C2semidirect
13. #10588340C2semidirect
14. #10588337C2semidirect
15. #10588336C2semidirect
72. C22×C4×C9Q8semidirect
401. C22×C4Dic18semidirect
459. C9#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#634882
C2×C4×Dic182
C4×C9×C22⋊C42
C4×#36762
#105886292
#105886282
#105886272
C4×C4⋊Dic92
C4×Dic9⋊C42
#105883412
#105883402
#105883372
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