Finite Group Databasebeta

← #11859354

Subgroups — #11859354

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596299C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5#10591149C214yesmaximal, complemented
6#10591148C214yesmaximal, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10591074C211yesmaximal, characteristic, complemented
9#10591059C211yesmaximal, characteristic, complemented
10#83794—31nomaximal
11#78655—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14#64155C412yes—
15#64147C412yes—
16#64146C412yes—
17#64144C412yes—
18C4×#638C2214yes—
19#64135C2211yescharacteristic
20C3×#948—24no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2212yescomplemented
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2212yescomplemented
27C2×#3710—24no—
28C2×#3710C2212yes—
29C2×#3710C2212yes—
30C3×#830C2214yescomplemented
31#63572C2214yescomplemented
32#63557C2214yes—
33#63555C2212yescomplemented
34#63553C2212yescomplemented
35C2×C3×#131—31no—
36#5828—31no—
37#5828—31no—
38#5828—61no—
39C2×#948D311yescharacteristic, complemented
40C22×D3×C8—31no—
41C22×D3×C8—31no—
42C3×#408—31no—
43#5234D311yescharacteristic, complemented
44#5127—34no—
45#5126—31no—
46#5126—31no—
47#5122—31no—
48#5119—31no—
49C8×#67—34no—
50#5102—31no—
51#5101—31no—
52#4728—34no—
53#67⋊C8—34no—
54C23×C3⋊D3C2×C411yescharacteristic
55C32×#41—22no—
56C32×#41—22no—
57C2×C32×Q8C2×C411yescharacteristic
58C2×C32×D4C2×C412yes—
59C2×C32×D4C2×C411yescharacteristic
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638C2×C414yes—
63C22×C3⋊Dic3C2×C411yescharacteristic
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2×C412yes—
67C2×C4×C3⋊D3C2312yes—
68#3757C2×C412yes—
69#3757C2×C414yes—
70#3752C2×C414yes—
71C4⋊(C3⋊Dic3)C2×C412yes—
72#3750C2×C414yes—
73C4×C3⋊Dic3C2312yes—
74C3×#208—22no—
75C3×#208—22no—
76C3×#208—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—24no—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85#3710—24no—
86#3710—24no—
87#2929—91noSylow
88C2×C3×#41—21no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—61no—
94C3×#131—64no—
95C2×C3×M16—31no—
96C2×C3×M16—31no—
97C2×C3×M16—32no—
98C22×C3×C8—31no—
99C22×C3×C8—32no—
100C22×C3×C8—31no—
101#948—24no—
102#946—32no—
103#946—32no—
104#946—62no—
105#938—32no—
106#938—32no—
107#938—62no—
108#937—32no—
109#937—32no—
110#937—62no—
111#935—32no—
112#935—32no—
113#935—62no—
114C4×#67—34no—
115C4×#67—34no—
116C4×#67—64no—
117#926—31no—
118#926—31no—
119#926—61no—
120C2×#208C2×D311yescharacteristic
121C2×#208C2×D311yescharacteristic
122C2×#208C2×D312yescomplemented
123C22×C3⋊C8C2×D311yescharacteristic
124C22×C3⋊C8C2×D311yescharacteristic
125C22×C3⋊C8C2×D312yescomplemented
126C2×D3×C8—32no—
127C2×D3×C8—32no—
128C2×D3×C8—32no—
129C2×D3×C8—32no—
130C2×D3×C8—64no—
131C2×D3×C8—64no—
132C3×C22⋊C8—34no—
133#830C2×D314yescomplemented
134(C2×D3)⋊C8—34no—
135(C2×D3)⋊C8—34no—
136#815—32no—
137#815—32no—
138Dic3⋊C8—34no—
139Dic3⋊C8—34no—
140C8×Dic3—32no—
141C8×Dic3—32no—
142C23×C32C22×C412yes—
143C23×C32C22×C411yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3⋊D3—24no—
146C22×C3⋊D3C22×C412yes—
147C32×Q8—22no—
148C32×D4—24no—
149C32×D4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C411yescharacteristic
154C2×C32×C4C2×D412yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157#638—28no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C22×C414yes—
160C2×C3⋊Dic3C22×C412yes—
161C4×C3⋊D3—24no—
162C4×C3⋊D3—22no—
163C4×C3⋊D3—22no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—22no—
167C3×C3⋊C8C2×D412yes—
168C3×C3⋊C8C2×D412yes—
169C2×#131—31no—
170C23×C8—91no—
171#525—91no—
172#435—94no—
173C8×D4—94no—
174#424—91no—
175#408—31no—
176#407—91no—
177#405—91no—
178C23×D3—31no—
179C23×D3—31no—
180C23×D3—61no—
181C3×#41—22no—
182C3×#41—22no—
183C3×#41—22no—
184C3×#41—22no—
185C3×#41—42no—
186C3×#41—42no—
187C2×C3×Q8—21no—
188C2×C3×Q8C4×D311yescharacteristic
189C2×C3×Q8C4×D311yescharacteristic
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4C4×D312yes—
193C2×C3×D4C4×D312yes—
194C2×C3×D4C4×D311yescharacteristic
195C2×C3×D4C4×D311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C2×#67—34no—
203C2×#67—34no—
204C2×#67—64no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—61no—
208C2×C4×D3—32no—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—122no—
219C2×C4×D3—122no—
220C3×M16—64no—
221C3×M16—62no—
222C3×M16—62no—
223C2×C3×C8—34no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—32no—
229C2×C3×C8—64no—
230C2×C3×C8—62no—
231#217—32no—
232#217—32no—
233#217—34no—
234#217—34no—
235#217—62no—
236#217—64no—
237(C2×D3)⋊C4—34no—
238(C2×D3)⋊C4—34no—
239(C2×D3)⋊C4—64no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243Dic3⋊C4—34no—
244Dic3⋊C4—34no—
245Dic3⋊C4—64no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—62no—
249#208—22no—
250#208—22no—
251#208—24no—
252C2×C3⋊C8—22no—
253C2×C3⋊C8—24no—
254C2×C3⋊C8#6714yescomplemented
255C2×C3⋊C8C22×D312yes—
256C2×C3⋊C8C22×D312yes—
257C2×C3⋊C8C22×D312yes—
258C2×C3⋊C8C22×D311yescharacteristic
259C2×C3⋊C8C22×D311yescharacteristic
260D3×C8—64no—
261D3×C8—64no—
262D3×C8—64no—
263D3×C8—64no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—24no—
267C22×C32C4×D412yes—
268C22×C32C23×C411yescharacteristic
269C2×C3⋊D3—28no—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3#13114yescomplemented
273C32×C4—22no—
274C32×C4C4×D412yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—24no—
279C2×#41D3211yescharacteristic
280C23×C4—91no—
281#131—64no—
282C2×M16—31no—
283C2×M16—32no—
284C2×M16—31no—
285C22×C8—31no—
286C22×C8—31no—
287C22×C8—32no—
288C22×C8—92no—
289C22×C8—92no—
290C22×C8—184no—
291#123—92no—
292C22⋊Q8—92no—
293#121—92no—
294#120—92no—
295C4×D4—94no—
296#117—91no—
297C4⋊C8—94no—
298C22⋊C8—34no—
299C22⋊C8—94no—
300#97—92no—
301C4×C8—92no—
302C23×C3—21no—
303C23×C3—22no—
304C23×C3C2×C4×D312yes—
305C23×C3C2×C4×D312yes—
306C23×C3C2×C4×D311yescharacteristic
307C23×C3C2×C4×D311yescharacteristic
308C22×D3—32no—
309C22×D3—32no—
310C22×D3—62no—
311C22×D3—64no—
312C22×D3—64no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—124no—
316C22×D3—122no—
317C3×Q8—22no—
318C3×Q8—22no—
319C3×Q8—42no—
320C3×D4—24no—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—42no—
325C3×D4—44no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4C2×C4×D312yes—
338C2×C3×C4C2×C4×D312yes—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4#23512yes—
342C2×C3×C4D3×D412yes—
343C2×C3×C4#23712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347#67—68no—
348#67—68no—
349#67—128no—
350C2×Dic3—34no—
351C2×Dic3—34no—
352C2×Dic3—32no—
353C2×Dic3—32no—
354C2×Dic3—64no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—122no—
359C4×D3—64no—
360C4×D3—64no—
361C4×D3—62no—
362C4×D3—62no—
363C4×D3—62no—
364C4×D3—62no—
365C4×D3—122no—
366C4×D3—122no—
367C4×D3—124no—
368C3×C8—32no—
369C3×C8—32no—
370C3×C8—62no—
371C3×C8—62no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—22no—
375C3⋊C8—22no—
376C3⋊C8C2×#6712yes—
377C3⋊C8C2×#6712yes—
378C2×C32—22no—
379C2×C32—42no—
380C2×C32C2×C4×D411yescharacteristic
381C2×C32C2×#13112yes—
382C3⋊D3—24no—
383C24—91no—
384#41—22no—
385#41—22no—
386C2×Q8#62411yescharacteristic
387C2×D4—94no—
388C2×D4#62412yes—
389C2×D4#62411yescharacteristic
390C22×C4—91no—
391C22×C4—92no—
392C22×C4—92no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4C2×D3212yes—
396C22×C4C2×D3211yescharacteristic
397M16—64no—
398M16—62no—
399M16—62no—
400C2×C8—31no—
401C2×C8—31no—
402C2×C8—34no—
403C2×C8—32no—
404C2×C8—32no—
405C2×C8—32no—
406C2×C8—64no—
407C2×C8—62no—
408C2×C8—184no—
409C2×C8—184no—
410C4⋊C4—92no—
411C4⋊C4—94no—
412C22⋊C4—92no—
413C22⋊C4—94no—
414C22⋊C4—94no—
415C42—92no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—22no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—42no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3#67⋊C412yes—
428C22×C3C4×#6712yes—
429C22×C3C22×C4×D311yescharacteristic
430C22×C3C22×C4×D311yescharacteristic
431C2×D3—34no—
432C2×D3—34no—
433C2×D3—64no—
434C2×D3—68no—
435C2×D3—68no—
436C2×D3—62no—
437C2×D3—62no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—128no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—42no—
449C3×C4#67⋊C412yes—
450C3×C4C4×#6712yes—
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23711yescharacteristic
454C3×C4C22×#6711yescharacteristic
455Dic3—62no—
456Dic3—64no—
457Dic3—64no—
458Dic3—62no—
459Dic3—122no—
460Dic3—124no—
461C32#292911yescharacteristic, complemented, Sylow
462C23—92no—
463C23—184no—
464C23—182no—
465C23C2×#62412yes—
466C23C2×#62411yescharacteristic
467Q8—22no—
468D4—24no—
469D4—22no—
470D4—188no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—94no—
474C2×C4—92no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—184no—
479C2×C4#380412yes—
480C2×C4C2×#62412yes—
481C2×C4C2×#62411yescharacteristic
482C2×C4D3×#6712yes—
483C2×C4C22×D3211yescharacteristic
484C8—32no—
485C8—32no—
486C8—62no—
487C8—62no—
488C8—62no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—42no—
494C2×C3—42no—
495C2×C3—42no—
496C2×C3—82no—
497C2×C3C2×#67⋊C411yescharacteristic
498C2×C3D3×#13112yes—
499C2×C3D3×#13112yes—
500C2×C3C2×C4×#6711yescharacteristic
501D3—64no—
502D3—64no—
503D3—124no—
504C22—22no—
505C22—24no—
506C22—22no—
507C22—94no—
508C22—188no—
509C22—182no—
510C22—182no—
511C22#6395212yes—
512C22C22×#62411yescharacteristic
513C4—22no—
514C4—184no—
515C4—182no—
516C4#6395212yes—
517C4C2×#380411yescharacteristic
518C4C2×D3×#6711yescharacteristic
519C3—21no—
520C3#7865511yescharacteristic, complemented
521C3#8379411yescharacteristic, complemented
522C2—22no—
523C2—42no—
524C2—184no—
525C2#1059544212yes—
526C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×#41C22
prime radical#10596299C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2929
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#948C2semidirect
3. C22×#3710C2semidirect
4. C3×#5234C2semidirect
5. #10591149C2semidirect
6. #10591148C2semidirect
7. #10591119C2semidirect
8. #10591074C2semidirect
9. #10591059C2semidirect
23. C2×C3×#208C22semidirect
26. C22×C3×C3⋊C8C22semidirect
30. C3×#830C22semidirect
31. #63572C22semidirect
33. #63555C22semidirect
34. #63553C22semidirect
39. C2×#948D3semidirect
43. #5234D3semidirect
79. C2×C3×C3⋊C8D4semidirect
122. C2×#208C2×D3semidirect
125. C22×C3⋊C8C2×D3semidirect
133. #830C2×D3semidirect
254. C2×C3⋊C8#67semidirect
272. C2×C3⋊D3#131semidirect
461. C32#2929semidirect
520. C3#78655semidirect
521. C3#83794semidirect

Maximal subgroups

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

subgroupindex
#105962992
C2×C3×#9482
C22×#37102
C3×#52342
#105911492
#105911482
#105911192
#105910742
#105910592
#837943
#786553