Finite Group Databasebeta

← #11773997

Subgroups — #11773997

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63850C211yesmaximal, characteristic
2C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589334C211yesmaximal, characteristic, complemented
5C3×#4469C211yesmaximal, characteristic, complemented
6#10589147C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#69920—31nomaximal
9#68146—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×#626C411yescharacteristic
12C2×#3752C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14C2×C3×D3×C8—21no—
15C2×#3724C411yescharacteristic
16C2×#3722C411yescharacteristic
17C2×(C2×D3)⋊Dic3C411yescharacteristic
18#63850—21no—
19#63850—21no—
20#63850—21no—
21#63850—21no—
22C2×#3711—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×(C2×D3)⋊C8—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×#929—31no—
30C2×#894—31no—
31C2×C3×C22⋊C8—31no—
32#5207—31no—
33#4726—31no—
34D3×C22⋊C8D311yescharacteristic, complemented
35C3×#324—31no—
36#4528—31no—
37#4469—31no—
38#4469D311yescharacteristic, complemented
39#4468—31no—
40#4468—31no—
41#4468—31no—
42#4468—31no—
43#4468—61no—
44C23×C3⋊D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×#626—21no—
57C2×#626—21no—
58C2×#626—42no—
59C2×C32×C8—21no—
60#3752—21no—
61#3752—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C3×D3×C8—42no—
68#3724—21no—
69#3724—21no—
70#3722—21no—
71#3722—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74#3711—42no—
75#1468—91noSylow
76C23×C3×C4—31no—
77C22×#67—31no—
78C22×D12—31no—
79C22×C4×D3C2×D311yescharacteristic
80C22×C3×C8—61no—
81C2×C3×C4⋊C4—31no—
82C2×#217—31no—
83#929—61no—
84#929—61no—
85#929—61no—
86#929—61no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—31no—
90C2×(C2×D3)⋊C4—31no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—61no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4C2×D311yescharacteristic
96C2×#208—61no—
97C2×ΓL(1,𝔽25)—61no—
98C2×D3×C8—21no—
99#894—61no—
100#894—61no—
101#894—61no—
102#894—61no—
103C3×C22⋊C8—21no—
104C3×C22⋊C8—31no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—61no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—61no—
112#830—61no—
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115(C2×D3)⋊C8—21no—
116(C2×D3)⋊C8—61no—
117C23×C32C22×C411yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3C22⋊C411yescharacteristic
128C22×C3×D3C22⋊C411yescharacteristic
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146#626—42no—
147#626—42no—
148C32×C8—41no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152C2×#123—91no—
153#407—91no—
154C2×C22⋊C8—31no—
155#324—31no—
156#324—91no—
157#323—91no—
158#323—91no—
159C24×C3—31no—
160C23×D3—31no—
161C23×D3—31no—
162C23×D3—61no—
163C23×D3C4×D311yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—122no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—122no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C22×Dic3C4×D311yescharacteristic
182C22×Dic3C4×D311yescharacteristic
183C22×Dic3C4×D311yescharacteristic
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—122no—
187C2×C4×D3—42no—
188C2×C4×D3D1211yescharacteristic
189C2×C4×D3D1211yescharacteristic
190C2×C4×D3#6711yescharacteristic
191C2×C4×D3#6711yescharacteristic
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—41no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—122no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200#217—61no—
201#217—61no—
202(C2×D3)⋊C4—61no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—121no—
213(C2×D3)⋊C4—121no—
214Dic3⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—61no—
219Dic3⋊C4—61no—
220#208—122no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226ΓL(1,𝔽25)—122no—
227D3×C8—42no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32#13111yescharacteristic
232C22×C32#13111yescharacteristic
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—81no—
237C2×C3⋊D3—81no—
238C2×C3×D3—21no—
239C2×C3×D3—21no—
240C2×C3×D3—21no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3#9912yes—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—41no—
249C3×Dic3—21no—
250C3×Dic3—21no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C22×D4—91no—
254C23×C4—31no—
255C2×M16—181no—
256C22×C8—61no—
257#123—181no—
258#123—181no—
259#123—181no—
260#123—181no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—91no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—91no—
266C22⋊C8—31no—
267C22⋊C8—31no—
268C22⋊C8—61no—
269C22⋊C8—91no—
270C22⋊C8—181no—
271C22⋊C8D3211yescharacteristic
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—62no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—121no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—22no—
284C22×D3—41no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—62no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—241no—
299C22×D3—241no—
300C22×D3(C2×D3)⋊C411yescharacteristic
301C22×D3(C2×D3)⋊C411yescharacteristic
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—31no—
305C2×C3×C4—31no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—81no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323#67—122no—
324#67—122no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3(C2×D3)⋊C411yescharacteristic
338C2×Dic3(C2×D3)⋊C411yescharacteristic
339D12—122no—
340D12—122no—
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—41no—
344C4×D3—41no—
345C3×C8—41no—
346C3×C8—41no—
347C3×C8—81no—
348C3×C8—121no—
349C3×C8—121no—
350C3⋊C8—41no—
351C3⋊C8—41no—
352C3⋊C8—121no—
353C3⋊C8—121no—
354C3⋊C8—241no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32#40811yescharacteristic
358C2×C32C2×#9911yescharacteristic
359C2×C32#41311yescharacteristic
360C3⋊D3—81no—
361C3×D3—22no—
362C3×D3—41no—
363C24—31no—
364C24—91no—
365C2×D4—181no—
366C2×D4—181no—
367C2×D4—362no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—91no—
376C22×C4—122no—
377C22×C4C2×D3211yescharacteristic
378M16—362no—
379C2×C8—21no—
380C2×C8—61no—
381C2×C8—61no—
382C2×C8—122no—
383C2×C8—181no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22⋊C4—181no—
393C22⋊C4—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—61no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—61no—
408C22×C3—61no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3D3×C22⋊C411yescharacteristic
412C22×C3#90111yescharacteristic
413C22×C3#90111yescharacteristic
414C22×C3#90111yescharacteristic
415C22×C3#90711yescharacteristic
416C22×C3C2×(C2×D3)⋊C411yescharacteristic
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—122no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—242no—
434C2×D3—241no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—242no—
439C2×D3#80612yes—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—61no—
447C3×C4—61no—
448C3×C4—121no—
449C3×C4—121no—
450Dic3—21no—
451Dic3—21no—
452Dic3—41no—
453Dic3—41no—
454Dic3—121no—
455Dic3—121no—
456Dic3—241no—
457C32#146811yescharacteristic, complemented, Sylow
458C23—31no—
459C23—31no—
460C23—62no—
461C23—61no—
462C23—61no—
463C23—121no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23—361no—
468C23—361no—
469C23C4×D3211yescharacteristic
470D4—362no—
471D4—362no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—41no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—181no—
486C2×C4—361no—
487C2×C4D3×D1211yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C8—41no—
490C8—121no—
491C8—121no—
492C8—361no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—62no—
503C2×C3—121no—
504C2×C3#472711yescharacteristic
505C2×C3D3×#9911yescharacteristic
506C2×C3#475111yescharacteristic
507C2×C3C2×#80611yescharacteristic
508C2×C3#511011yescharacteristic
509C2×C3#513211yescharacteristic
510D3—22no—
511D3—41no—
512D3—242no—
513D3—241no—
514D3—241no—
515C22—21no—
516C22—21no—
517C22—32no—
518C22—61no—
519C22—61no—
520C22—61no—
521C22—61no—
522C22—61no—
523C22—122no—
524C22—122no—
525C22—361no—
526C22—361no—
527C22—361no—
528C22—721no—
529C22—721no—
530C22#6380311yescharacteristic
531C22#6380411yescharacteristic
532C22D3×(C2×D3)⋊C411yescharacteristic
533C4—21no—
534C4—21no—
535C4—61no—
536C4—61no—
537C4—121no—
538C4—121no—
539C4—361no—
540C3—21no—
541C3#6814611yescharacteristic, complemented
542C3#6992011yescharacteristic, complemented
543C2—21no—
544C2—21no—
545C2—62no—
546C2—121no—
547C2—721no—
548C2D3×#80611yescharacteristic
549C2#1059095311yescharacteristic
550C2#1059100711yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#626C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D3×C22⋊C8C2semidirect
3. #10591154C2semidirect
4. #10589334C2semidirect
5. C3×#4469C2semidirect
6. #10589147C2semidirect
7. #10589146C2semidirect
34. D3×C22⋊C8D3semidirect
38. #4469D3semidirect
457. C32#1468semidirect
541. C3#68146semidirect
542. C3#69920semidirect

Maximal subgroups

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

subgroupindex
C2×#638502
C3×D3×C22⋊C82
#105911542
#105893342
C3×#44692
#105891472
#105891462
#699203
#681463