Finite Group Databasebeta

← #11775398

Subgroups — #11775398

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5606C211yesmaximal, characteristic
2#10591295C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71709—31nomaximal
9#68305—31nomaximal
10C2×C3×#237C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C32×#121C2211yescharacteristic
13C3×#938C411yescharacteristic, complemented
14C3×#937—21no—
15C3×D4×Dic3—21no—
16C3×#924C2211yescharacteristic
17C3×#897C411yescharacteristic, complemented
18C3×#892C411yescharacteristic, complemented
19C3×#883—21no—
20C3×#67⋊C4—21no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3711—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28(C2×D3)⋊(C3⋊C8)—21no—
29C3×#525—31no—
30#5606D311yescharacteristic
31#5212—31no—
32#5207—31no—
33#4726—31no—
34#4667—31no—
35C3×#327—31no—
36#4538—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4537D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C3×#237—42no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×Dic6C2×C411yescharacteristic
61C32×C4⋊C4C2×C411yescharacteristic
62C32×C22⋊C4—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75#3711—42no—
76#1513—91noSylow
77C2×C3×#41—31no—
78C23×C3×C4—31no—
79C2×#237Dic311yescharacteristic, complemented
80C22×C4×D3C2×D311yescharacteristic
81C3×#123—61no—
82C3×C22⋊Q8—31no—
83C3×C22⋊Q8—31no—
84C3×#121—21no—
85C3×#121—31no—
86C3×#121C2×D311yescharacteristic
87C3×#121C2×D311yescharacteristic
88C3×#120—61no—
89C3×C4×D4—61no—
90C3×C4×D4—61no—
91C3×#117—31no—
92C2×#217—61no—
93#938Dic311yescharacteristic, complemented
94#937—21no—
95D4×Dic3—21no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—61no—
98#924C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×#208—61no—
101C2×ΓL(1,𝔽25)—61no—
102#897Dic311yescharacteristic, complemented
103#892Dic311yescharacteristic, complemented
104#883—21no—
105#67⋊C4—21no—
106C3×C22⋊C8—31no—
107C3×#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—61no—
111C3⋊#95C2×D311yescharacteristic
112#830—31no—
113#830—31no—
114#830—61no—
115#830—61no—
116#830C2×D311yescharacteristic
117(C2×D3)⋊C8—61no—
118C23×C32—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3C22⋊C411yescharacteristic
125C22×C3×D3C22⋊C411yescharacteristic
126C32×D4—41no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C3×#67—42no—
137C3×#67—42no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3C22⋊C411yescharacteristic
146C2×C3×Dic3C22⋊C411yescharacteristic
147C3×C4×D3—22no—
148C3×C4×D3—22no—
149C3×C4×D3—41no—
150C3×C4×D3—41no—
151C3×Dic6—41no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—41no—
154#525—31no—
155#407—91no—
156#380—91no—
157#328—91no—
158#328—91no—
159#327—31no—
160#327—91no—
161C24×C3—31no—
162C23×D3#6711yescharacteristic
163C3×#41—122no—
164C2×C3×Q8—31no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—41no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4C4×D311yescharacteristic
172C2×C3×D4C2×Dic311yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—122no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C2×#67—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—121no—
191C22×Dic3#6711yescharacteristic
192#237—42no—
193C2×C4×D3—42no—
194C2×C4×D3C2×Dic311yescharacteristic
195C2×C4×D3C2×Dic311yescharacteristic
196C2×C4×D3#6711yescharacteristic
197C2×C4×D3#6711yescharacteristic
198C2×Dic6C2×Dic311yescharacteristic
199C2×C3×C8—61no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C4×D311yescharacteristic
205C3×C4⋊C4C2×Dic311yescharacteristic
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—41no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C42—61no—
214#217—21no—
215#217—21no—
216#217—122no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—122no—
220C4⋊Dic3—21no—
221C4⋊Dic3—122no—
222C4⋊Dic3C2×Dic311yescharacteristic
223Dic3⋊C4—21no—
224Dic3⋊C4—122no—
225C4×Dic3—21no—
226#208—122no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231ΓL(1,𝔽25)—122no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32AGL(1,ℤ/8)11yescharacteristic
239C22×C32#13711yescharacteristic
240C2×C3×D3—21no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3—21no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C32×C4—21no—
249C32×C4—21no—
250C32×C4—41no—
251C3⋊Dic3—81no—
252C3×Dic3—21no—
253C3×Dic3—41no—
254C3×Dic3—41no—
255C3×Dic3—81no—
256C3×Dic3#9912yes—
257C2×#41—31no—
258C23×C4—31no—
259C2×M16—181no—
260#123—61no—
261C22⋊Q8—31no—
262C22⋊Q8—31no—
263#121—31no—
264#121D3211yescharacteristic
265#120—61no—
266C4×D4—61no—
267C4×D4—61no—
268#117—31no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—181no—
271C22⋊C8—31no—
272C22⋊C8—91no—
273C22⋊C8—181no—
274#95—31no—
275#95—91no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—31no—
280C23×C3—31no—
281C23×C3—41no—
282C23×C3—61no—
283C23×C3—61no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3#21711yescharacteristic
293C22×D3#21711yescharacteristic
294C3×Q8—121no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—81no—
302C3×D4—81no—
303C3×D4—81no—
304C3×D4—122no—
305C3×D4—122no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—31no—
311C2×C3×C4—31no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—81no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—122no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C22×Dic311yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331#67—42no—
332#67—42no—
333C2×Dic3—22no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—42no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—122no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—241no—
348C2×Dic3—241no—
349C2×Dic3#21711yescharacteristic
350C2×Dic3#21711yescharacteristic
351C4×D3—22no—
352C4×D3—22no—
353C4×D3—41no—
354C4×D3—41no—
355Dic6—41no—
356C3×C8—121no—
357C3⋊C8—41no—
358C3⋊C8—121no—
359C3⋊C8—121no—
360C3⋊C8—241no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—81no—
364C2×C32C2×#9911yescharacteristic
365C2×C32#41711yescharacteristic
366C2×C32#42111yescharacteristic
367C3×D3—41no—
368C3×D3—41no—
369C24—31no—
370#41—122no—
371C2×Q8—31no—
372C2×D4—21no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4D3×Dic311yescharacteristic
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—122no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386M16—362no—
387C2×C8—61no—
388C2×C8—181no—
389C4⋊C4—31no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—362no—
393C4⋊C4D3×Dic311yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—61no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—61no—
399C22⋊C4—362no—
400C42—61no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—61no—
417C22×C3—61no—
418C22×C3—61no—
419C22×C3—61no—
420C22×C3—61no—
421C22×C3—61no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3—81no—
425C22×C3—122no—
426C22×C3—122no—
427C22×C3D3×C22⋊C411yescharacteristic
428C22×C3#91111yescharacteristic
429C22×C3#91511yescharacteristic
430C22×C3#94911yescharacteristic
431C22×C3#95111yescharacteristic
432C22×C3C2×#21711yescharacteristic
433C2×D3—21no—
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—21no—
437C2×D3—21no—
438C2×D3—21no—
439C2×D3—42no—
440C2×D3—42no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—32no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—61no—
451C3×C4—81no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4—241no—
455Dic3—21no—
456Dic3—41no—
457Dic3—41no—
458Dic3—81no—
459Dic3—241no—
460Dic3—241no—
461Dic3—242no—
462Dic3#83412yes—
463C32#151311yescharacteristic, complemented, Sylow
464C23—21no—
465C23—31no—
466C23—31no—
467C23—61no—
468C23—61no—
469C23—121no—
470C23—121no—
471C23D3×#6711yescharacteristic
472Q8—121no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—122no—
477D4—122no—
478C2×C4—21no—
479C2×C4—31no—
480C2×C4—31no—
481C2×C4—41no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—122no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4—361no—
496C2×C4C2×D3×Dic311yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C8—121no—
499C8—361no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3—121no—
512C2×C3—121no—
513C2×C3—161no—
514C2×C3D3×#9911yescharacteristic
515C2×C3#477111yescharacteristic
516C2×C3#482111yescharacteristic
517C2×C3C2×#83411yescharacteristic
518C2×C3#523211yescharacteristic
519C2×C3#523611yescharacteristic
520D3—41no—
521D3—41no—
522C22—21no—
523C22—21no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—61no—
528C22—61no—
529C22—61no—
530C22—61no—
531C22—61no—
532C22—61no—
533C22—122no—
534C22—122no—
535C22#6392511yescharacteristic
536C22#6392911yescharacteristic
537C22D3×#21711yescharacteristic
538C4—21no—
539C4—21no—
540C4—32no—
541C4—41no—
542C4—61no—
543C4—121no—
544C4—121no—
545C4—241no—
546C4—721no—
547C3—21no—
548C3#6830511yescharacteristic, complemented
549C3#7170911yescharacteristic, complemented
550C2—21no—
551C2—21no—
552C2—81no—
553C2—121no—
554C2—121no—
555C2#1059141411yescharacteristic
556C2D3×#83411yescharacteristic
557C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5606C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591295C2semidirect
3. #10591154C2semidirect
4. #10589403C2semidirect
5. C3×#4537C2semidirect
6. #10589153C2semidirect
7. #10589152C2semidirect
10. C2×C3×#237C4semidirect
13. C3×#938C4semidirect
17. C3×#897C4semidirect
18. C3×#892C4semidirect
41. #4537D3semidirect
79. C2×#237Dic3semidirect
93. #938Dic3semidirect
102. #897Dic3semidirect
103. #892Dic3semidirect
463. C32#1513semidirect
548. C3#68305semidirect
549. C3#71709semidirect

Maximal subgroups

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

subgroupindex
C3×#56062
#105912952
#105911542
#105894032
C3×#45372
#105891532
#105891522
#717093
#683053