Finite Group Databasebeta

← #11906005

Subgroups — #11906005

Order 1152.

2214 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63716C211yesmaximal, characteristic, complemented
2C2×#63713C211yesmaximal, characteristic, complemented
3C9×#536C211yesmaximal, characteristic, complemented
4#10589934C211yesmaximal, characteristic, complemented
5C2×#63506C211yesmaximal, characteristic, complemented
6#10589826C212yesmaximal, complemented
7D9×C4⋊Q8C212yesmaximal, complemented
8#10589777C212yesmaximal, complemented
9#10589770C212yesmaximal, complemented
10#10589757C218yesmaximal, complemented
11#10589734C214yesmaximal, complemented
12#10589733C214yesmaximal, complemented
13#10589628C211yesmaximal, characteristic, complemented
14#10589624C211yesmaximal, characteristic, complemented
15#86340—31nomaximal
16C2×C9×#41C2211yescharacteristic
17C22×Q8×C9C2211yescharacteristic
18#63716—28no—
19#63713—28no—
20C2×#3701C2212yes—
21C2×#3701C2212yes—
22C2×Q8×D9C2212yes—
23C2×Q8×D9C2212yes—
24C2×Q8×D9C2212yes—
25C2×#3699C2214yes—
26C2×#3699C2212yes—
27C2×#3697C2212yes—
28C2×#3697C2214yes—
29C2×#3697C2211yescharacteristic
30C2×#3697C2211yescharacteristic
31C22×Dic18C2212yes—
32C22×Dic18C2211yescharacteristic
33C9×C4⋊Q8C2212yes—
34C9×#124C2212yes—
35C9×#123C2214yes—
36C9×C22⋊Q8C2214yes—
37C9×#117C2211yescharacteristic
38#63509C2211yescharacteristic
39#63506C2214yes—
40#63506C2212yes—
41#63506C2212yes—
42#63506C2211yescharacteristic
43#63502C2211yescharacteristic
44#63501C2214yes—
45#63498C2211yescharacteristic
46C4×#611C2214yes—
47C2×Dic9⋊C4C2214yes—
48C2×C4×Dic9C2211yescharacteristic
49#63459C2214yes—
50#63458C2218yes—
51#63456C2218yes—
52#63455C2212yes—
53C4⋊C4×D9C2218yes—
54#63450C2218yes—
55#63449C2212yes—
56#63448C2214yes—
57#63446C2218yes—
58#63445C2218yes—
59#611⋊C4C2218yes—
60#611⋊C4C2214yes—
61#63440C2218yes—
62#63437C2212yes—
63#63434C2212yes—
64C42×D9C2212yes—
65#63431C2212yes—
66C2×#1010—31no—
67C2×#1007—31no—
68C3×#536D311yescharacteristic
69#5832—31no—
70C2×#944—31no—
71#5724—32no—
72D3×C4⋊Q8—32no—
73#5675—32no—
74#5668—32no—
75#5655—38no—
76#5632—34no—
77#5631—34no—
78#5526—31no—
79#5522—31no—
80C9×#41—24no—
81C2×Q8×C9—24no—
82C2×Q8×C9C2312yes—
83C2×Q8×C9C2312yes—
84C2×Q8×C9C2311yescharacteristic
85C2×D4×C9C2311yescharacteristic
86C2×D4×C9C2312yes—
87C22×C4×C9C2312yes—
88C22×C4×C9C2312yes—
89C22×C4×C9C2311yescharacteristic
90C2×#611C2314yes—
91C2×#611C2312yes—
92C2×#611C2314yes—
93C2×#611C2312yes—
94C22×Dic9C2312yes—
95C22×Dic9C2314yes—
96C22×Dic9C2312yes—
97#3701—28no—
98#3701—28no—
99Q8×D9—28no—
100Q8×D9—28no—
101Q8×D9—28no—
102#3699—216no—
103#3699—28no—
104#3697—24no—
105#3697—216no—
106#3697—28no—
107#3697D418yescomplemented
108C2×D36C2311yescharacteristic
109C2×D36C2314yes—
110C2×D36C2311yescharacteristic
111C2×C4×D9C2312yes—
112C2×C4×D9C2314yes—
113C2×C4×D9C2314yes—
114C2×C4×D9C2314yes—
115C2×C4×D9C2314yes—
116C2×C4×D9C2312yes—
117C2×Dic18—24no—
118C2×Dic18—28no—
119C2×Dic18C2311yescharacteristic
120C2×Dic18C2312yes—
121C2×Dic18C2312yes—
122C2×Dic18C2314yes—
123C2×Dic18C2314yes—
124C2×Dic18C2311yescharacteristic
125C9×C4⋊C4C2312yes—
126C9×C4⋊C4C2318yes—
127C9×C22⋊C4C2312yes—
128C9×C22⋊C4C2318yes—
129C42×C9C2312yes—
130#3676C2314yes—
131(C2×D9)⋊C4C2314yes—
132(C2×D9)⋊C4C2314yes—
133(C2×D9)⋊C4C2318yes—
134C4⋊Dic9C2318yes—
135Dic9⋊C4C2314yes—
136Dic9⋊C4C2318yes—
137Dic9⋊C4C2318yes—
138Dic9⋊C4C2314yes—
139C4×Dic9C2312yes—
140C4×Dic9C2311yescharacteristic
141C4×Dic9C2311yescharacteristic
142C4×Dic9C2314yes—
143#3499—91noSylow
144C2×C3×#41C2×D311yescharacteristic
145C22×C3×Q8C2×D311yescharacteristic
146#1010—68no—
147#1007—68no—
148C2×#239—32no—
149C2×#239—32no—
150C2×D3×Q8—32no—
151C2×D3×Q8—32no—
152C2×D3×Q8—32no—
153C2×#237—34no—
154C2×#237—32no—
155C2×#235—31no—
156C2×#235—34no—
157C2×#235—31no—
158C2×#235—32no—
159C22×Dic6—32no—
160C22×Dic6—31no—
161C3×C4⋊Q8C2×D312yes—
162C3×#124C2×D312yes—
163C3×#123C2×D314yes—
164C3×C22⋊Q8C2×D314yes—
165C3×#117C2×D311yescharacteristic
166#947—31no—
167#944—34no—
168#944—32no—
169#944—32no—
170#944—31no—
171#940—31no—
172#939—34no—
173#936—31no—
174C4×#67—34no—
175C2×Dic3⋊C4—34no—
176C2×C4×Dic3—31no—
177#897—34no—
178#896—38no—
179#894—38no—
180#893—32no—
181D3×C4⋊C4—38no—
182#888—38no—
183#887—32no—
184#886—34no—
185#884—38no—
186#883—38no—
187#67⋊C4—38no—
188#67⋊C4—34no—
189#878—38no—
190#875—32no—
191#872—32no—
192C42×D3—32no—
193#869—32no—
194C23×C9C2412yes—
195C23×C9C2411yescharacteristic
196C22×D9C2412yes—
197C22×D9C2412yes—
198Q8×C9—22no—
199Q8×C9—24no—
200Q8×C9—24no—
201D4×C9—24no—
202D4×C9—22no—
203C2×C4×C9—24no—
204C2×C4×C9—24no—
205C2×C4×C9C2×D414yes—
206C2×C4×C9C2414yes—
207C2×C4×C9C2414yes—
208C2×C4×C9C2412yes—
209C2×C4×C9C2411yescharacteristic
210C2×C4×C9C2411yescharacteristic
211#611—24no—
212#611—28no—
213#611—28no—
214#611C2×D418yes—
215C2×Dic9—24no—
216C2×Dic9—28no—
217C2×Dic9—24no—
218C2×Dic9C2412yes—
219C2×Dic9C2414yes—
220C2×Dic9C2412yes—
221C2×Dic9C2412yes—
222C2×Dic9C2412yes—
223D36—28no—
224D36—22no—
225D36C2×D414yes—
226C4×D9—28no—
227C4×D9—28no—
228C4×D9—24no—
229C4×D9—28no—
230C4×D9—28no—
231C4×D9C2×D418yes—
232Dic18—24no—
233Dic18—24no—
234Dic18—22no—
235Dic18—28no—
236Dic18—28no—
237Dic18C2×D414yes—
238C2×2−1+4—91no—
239C2×2−1+4—91no—
240D4×Q8—94no—
241#547—98no—
242#547—94no—
243#536—92no—
244#536—92no—
245#536—91no—
246#536D911yescharacteristic, complemented
247#532—91no—
248#532—92no—
249C2×C4⋊Q8—91no—
250C2×C4⋊Q8—92no—
251C4×#41—91no—
252C3×#41—24no—
253C2×C3×Q8—24no—
254C2×C3×Q8C22×D312yes—
255C2×C3×Q8C22×D312yes—
256C2×C3×Q8C22×D311yescharacteristic
257C2×C3×D4C22×D311yescharacteristic
258C2×C3×D4C22×D312yes—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C2×#67—32no—
263C2×#67—34no—
264C2×#67—34no—
265C2×#67—32no—
266C22×Dic3—34no—
267C22×Dic3—32no—
268C22×Dic3—32no—
269#239—68no—
270#239—68no—
271D3×Q8—68no—
272D3×Q8—68no—
273D3×Q8—68no—
274#237—68no—
275#237—616no—
276#235—38no—
277#235—68no—
278#235—616no—
279#235—64no—
280C2×D12—31no—
281C2×D12—31no—
282C2×D12—34no—
283C2×C4×D3—32no—
284C2×C4×D3—34no—
285C2×C4×D3—34no—
286C2×C4×D3—34no—
287C2×C4×D3—34no—
288C2×C4×D3—32no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—32no—
292C2×Dic6—34no—
293C2×Dic6—34no—
294C2×Dic6—32no—
295C2×Dic6—68no—
296C2×Dic6—64no—
297C3×C4⋊C4C22×D312yes—
298C3×C4⋊C4C22×D318yes—
299C3×C22⋊C4C22×D318yes—
300C3×C22⋊C4C22×D312yes—
301C3×C42C22×D312yes—
302#217—34no—
303(C2×D3)⋊C4—34no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—34no—
306C4⋊Dic3—38no—
307Dic3⋊C4—34no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—34no—
311C4×Dic3—31no—
312C4×Dic3—34no—
313C4×Dic3—31no—
314C4×Dic3—32no—
315C22×C9—22no—
316C22×C9—22no—
317C22×C9—24no—
318C22×C9C22×D412yes—
319C22×C9C2511yescharacteristic
320C2×D9—24no—
321C2×D9—22no—
322C2×D9—24no—
323C2×D9C22×D414yes—
324C4×C9—22no—
325C4×C9—24no—
326C4×C9—24no—
327C4×C9C22×D412yes—
328C4×C9C22×D412yes—
329Dic9—22no—
330Dic9—24no—
331Dic9—22no—
332Dic9C22×D414yes—
333Dic92−1+414yescomplemented
3342−1+4—188no—
3352−1+4—188no—
336C2×#41—92no—
337C2×#41—92no—
338C2×#41—92no—
339C2×#41—94no—
340C2×#41—91no—
341C2×#41—91no—
342C2×#41—92no—
343C2×#41—94no—
344C2×#41C2×D911yescharacteristic
345C22×Q8—92no—
346C22×Q8—92no—
347C22×Q8—92no—
348C22×Q8—91no—
349C22×Q8—92no—
350C22×Q8C2×D911yescharacteristic
351C4⋊Q8—91no—
352C4⋊Q8—92no—
353C4⋊Q8—92no—
354C4⋊Q8—94no—
355C4⋊Q8—98no—
356C4⋊Q8—92no—
357C4⋊Q8C2×D912yes—
358#127—91no—
359#124—91no—
360#124—91no—
361#124—92no—
362#124C2×D912yes—
363#123—98no—
364#123—98no—
365#123—94no—
366#123C2×D914yes—
367C22⋊Q8—98no—
368C22⋊Q8—94no—
369C22⋊Q8—98no—
370C22⋊Q8C2×D914yes—
371#121—94no—
372#121—98no—
373C4×Q8—92no—
374C4×D4—94no—
375C4×D4—92no—
376C4×D4—94no—
377C4×D4—98no—
378#117—92no—
379#117C2×D911yescharacteristic
380C2×C4⋊C4—94no—
381C2×C4⋊C4—98no—
382C2×C42—91no—
383C2×C42—92no—
384C23×C3C23×D312yes—
385C23×C3C23×D311yescharacteristic
386C22×D3—32no—
387C22×D3—32no—
388C3×Q8—22no—
389C3×Q8—24no—
390C3×Q8—24no—
391C3×D4—24no—
392C3×D4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4D3×D414yes—
396C2×C3×C4C23×D314yes—
397C2×C3×C4C23×D314yes—
398C2×C3×C4C23×D312yes—
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—38no—
402#67—68no—
403#67—68no—
404#67—64no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—34no—
409C2×Dic3—32no—
410C2×Dic3—68no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413D12—34no—
414D12—68no—
415D12—62no—
416C4×D3—38no—
417C4×D3—68no—
418C4×D3—68no—
419C4×D3—68no—
420C4×D3—68no—
421C4×D3—64no—
422Dic6—34no—
423Dic6—68no—
424Dic6—68no—
425Dic6—64no—
426Dic6—64no—
427Dic6—62no—
428C2×C9—22no—
429C2×C9—42no—
430C2×C9C23×D411yescharacteristic
431C2×C9C2×2−1+412yes—
432D9—24no—
433D9—42no—
434#41—24no—
435#41—98no—
436#41—1816no—
437#41—188no—
438#41—188no—
439#41—188no—
440#41—1816no—
441#41—188no—
442#41—184no—
443C2×Q8—24no—
444C2×Q8—91no—
445C2×Q8—94no—
446C2×Q8—94no—
447C2×Q8—92no—
448C2×Q8—91no—
449C2×Q8—92no—
450C2×Q8—188no—
451C2×Q8—188no—
452C2×Q8—188no—
453C2×Q8—188no—
454C2×Q8—184no—
455C2×Q8C22×D912yes—
456C2×Q8C22×D911yescharacteristic
457C2×Q8C22×D912yes—
458C2×D4—92no—
459C2×D4—94no—
460C2×D4—94no—
461C2×D4—92no—
462C2×D4—91no—
463C2×D4—94no—
464C2×D4—91no—
465C2×D4C22×D912yes—
466C2×D4C22×D911yescharacteristic
467C22×C4—92no—
468C22×C4—92no—
469C22×C4—92no—
470C22×C4—94no—
471C22×C4—94no—
472C22×C4—94no—
473C22×C4—94no—
474C22×C4—94no—
475C22×C4—92no—
476C22×C4C22×D912yes—
477C22×C4C22×D912yes—
478C22×C4C22×D911yescharacteristic
479C4⋊C4—94no—
480C4⋊C4—98no—
481C4⋊C4—98no—
482C4⋊C4—98no—
483C4⋊C4—94no—
484C4⋊C4C22×D918yes—
485C4⋊C4C22×D912yes—
486C22⋊C4—94no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C22⋊C4—98no—
490C22⋊C4C22×D912yes—
491C22⋊C4C22×D918yes—
492C42—91no—
493C42—91no—
494C42—94no—
495C42—92no—
496C42C22×D912yes—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—24no—
500C22×C3C2×D3×D412yes—
501C22×C3C24×D311yescharacteristic
502C2×D3—34no—
503C2×D3—64no—
504C2×D3—62no—
505C2×D3—64no—
506C3×C4—22no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4C2×D3×D412yes—
510C3×C4C2×D3×D412yes—
511Dic3—34no—
512Dic3—34no—
513Dic3—62no—
514Dic3—64no—
515Dic3—62no—
516C9#349911yescharacteristic, complemented, Sylow
517C23—92no—
518C23—92no—
519C23C23×D912yes—
520C23C23×D911yescharacteristic
521Q8—24no—
522Q8—24no—
523Q8—22no—
524Q8—94no—
525Q8—188no—
526Q8—188no—
527Q8—184no—
528Q8—182no—
529Q8—184no—
530D4—24no—
531D4—22no—
532D4—98no—
533D4—94no—
534D4—188no—
535D4—188no—
536D4—188no—
537D4—184no—
538D4—182no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—98no—
544C2×C4—92no—
545C2×C4—92no—
546C2×C4—94no—
547C2×C4—188no—
548C2×C4—188no—
549C2×C4—188no—
550C2×C4—188no—
551C2×C4—188no—
552C2×C4—184no—
553C2×C4—184no—
554C2×C4—184no—
555C2×C4D4×D914yes—
556C2×C4C23×D914yes—
557C2×C4C23×D912yes—
558C2×C4C23×D914yes—
559C2×C4C23×D911yescharacteristic
560C2×C4C23×D911yescharacteristic
561C2×C3—22no—
562C2×C3—42no—
563C2×C3C22×D3×D411yescharacteristic
564C2×C3D3×2−1+412yes—
565D3—64no—
566D3—122no—
567C22—22no—
568C22—22no—
569C22—24no—
570C22—94no—
571C22—184no—
572C22—182no—
573C22—184no—
574C22C2×D4×D912yes—
575C22C24×D911yescharacteristic
576C4—22no—
577C4—24no—
578C4—24no—
579C4—94no—
580C4—94no—
581C4—182no—
582C4—184no—
583C4—182no—
584C4C2×D4×D912yes—
585C4C2×D4×D912yes—
586C3#8634011yescharacteristic
587C2—22no—
588C2—42no—
589C2—184no—
590C2—362no—
591C2C22×D4×D911yescharacteristic
592C2D9×2−1+412yes—
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#536C2
hypercenter#536D9
hypocenterC9#3499
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C2×#63716C2semidirect
2. C2×#63713C2semidirect
3. C9×#536C2semidirect
4. #10589934C2semidirect
5. C2×#63506C2semidirect
6. #10589826C2semidirect
7. D9×C4⋊Q8C2semidirect
8. #10589777C2semidirect
9. #10589770C2semidirect
10. #10589757C2semidirect
11. #10589734C2semidirect
12. #10589733C2semidirect
13. #10589628C2semidirect
14. #10589624C2semidirect
107. #3697D4semidirect
246. #536D9semidirect
333. Dic92−1+4semidirect
516. C9#3499semidirect

Maximal subgroups

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

subgroupindex
C2×#637162
C2×#637132
C9×#5362
#105899342
C2×#635062
#105898262
D9×C4⋊Q82
#105897772
#105897702
#105897572
#105897342
#105897332
#105896282
#105896242
#863403