Finite Group Databasebeta

← #11775401

Subgroups — #11775401

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589154C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#69979—31nomaximal
7#69508—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3828C411yescharacteristic, complemented
10#64162—21no—
11#64139C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13#64138—21no—
14C4×#638—21no—
15C4×#638—21no—
16#64135C411yescharacteristic, complemented
17#64133C411yescharacteristic, complemented
18#64133C2211yescharacteristic
19C2×C3×#217—21no—
20C2×C3×C4⋊Dic3—21no—
21C2×C3×#208—21no—
22C3×C3⋊#95C2212yes—
23C3×#830—21no—
24C3×#830C2212yes—
25#5791—31no—
26#5791—31no—
27#5791—61no—
28C3×#407—31no—
29C3×#380—31no—
30#5212D311yescharacteristic, complemented
31#5207D311yescharacteristic, complemented
32#4470—32no—
33#4467—32no—
34#4452—32no—
35#4451—32no—
36C24×C32D411yescharacteristic
37C22×C32×C4—42no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C2×#638—21no—
46C2×#638—21no—
47#3828—42no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634C2×C411yescharacteristic
51C22×C3×Dic3—22no—
52#3757—21no—
53#3757—21no—
54#3757—21no—
55#3752—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59#3750—21no—
60#3750—21no—
61C4×C3⋊Dic3—21no—
62C3×#217—42no—
63C3×C4⋊Dic3—42no—
64C3×#208—42no—
65C2×C3×C3⋊C8—22no—
66#1513—91noSylow
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C2×D311yescharacteristic
70C2×#235—31no—
71C2×#235—31no—
72C2×#235—61no—
73C2×C3×M16—61no—
74C2×C3×C4⋊C4—61no—
75C2×C3×C22⋊C4—61no—
76#953—62no—
77#953—61no—
78#953—61no—
79C2×#217—21no—
80#930—31no—
81#930—31no—
82#930—31no—
83#930—31no—
84#930—61no—
85#930—61no—
86#929—62no—
87#929—61no—
88#929—61no—
89C4×#67—62no—
90C4×#67—62no—
91C4×#67—61no—
92C4×#67—61no—
93C4×#67—61no—
94C4×#67—61no—
95#926—31no—
96#926—31no—
97#926—61no—
98C2×C4⋊Dic3—21no—
99#924—31no—
100#924—31no—
101#924—31no—
102#924—31no—
103#924—61no—
104#924—61no—
105C2×#208—21no—
106C3×C22⋊C8—32no—
107C3×C22⋊C8—61no—
108C3×#95—32no—
109C3⋊#95C2×D312yes—
110#830—21no—
111#830C2×D312yes—
112C23×C32—21no—
113C23×C32—21no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32C22⋊C411yescharacteristic
117C23×C32C22⋊C411yescharacteristic
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C22⋊C411yescharacteristic
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130#638—42no—
131#638—42no—
132#638—41no—
133#638—41no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—41no—
138C4×C3⋊D3—42no—
139#634—41no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C3×C3⋊C8—42no—
144#525—91no—
145#407—31no—
146#380—31no—
147#328—92no—
148#327—92no—
149C24×C3—21no—
150C24×C3D1211yescharacteristic
151C24×C3#6711yescharacteristic
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—42no—
159C22×C3×C4—42no—
160C22×C3×C4—44no—
161C22×C3×C4—62no—
162C22×C3×C4C4×D311yescharacteristic
163C22×C3×C4C4×D311yescharacteristic
164C22×C3×C4C4×D311yescharacteristic
165C22×C3×C4C4×D311yescharacteristic
166C22×C3×C4D1211yescharacteristic
167C22×C3×C4D1211yescharacteristic
168C22×C3×C4D1211yescharacteristic
169C22×C3×C4#6711yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—62no—
175C2×#67—62no—
176C2×#67—62no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—61no—
182C2×#67—61no—
183C22×Dic3—22no—
184#235—124no—
185#235—122no—
186#235—122no—
187C2×D12—31no—
188C2×D12—31no—
189C2×D12—61no—
190C2×C4×D3—62no—
191C2×C4×D3—61no—
192C2×C4×D3—61no—
193C2×Dic6—31no—
194C2×Dic6—31no—
195C2×Dic6—61no—
196C3×M16—122no—
197C2×C3×C8—62no—
198C3×C4⋊C4—122no—
199C3×C22⋊C4—122no—
200#217—42no—
201#217—62no—
202#217—62no—
203#217—62no—
204#217—61no—
205#217—61no—
206#217—61no—
207#217—61no—
208#217—61no—
209#217—61no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216C4⋊Dic3—31no—
217C4⋊Dic3—31no—
218C4⋊Dic3—31no—
219C4⋊Dic3—31no—
220C4⋊Dic3—42no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229C4×Dic3—62no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232#208—42no—
233C2×C3⋊C8—22no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32—21no—
239C22×C32—21no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—42no—
243C22×C32—42no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C22×C32#13711yescharacteristic
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C2×C3⋊D3—41no—
250C32×C4—21no—
251C32×C4—21no—
252C32×C4—21no—
253C32×C4#9912yes—
254C3⋊Dic3—41no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3×Dic3—82no—
258C2×#41—91no—
259C23×C4D3211yescharacteristic
260C2×M16—61no—
261#123—181no—
262C22⋊Q8—91no—
263C22⋊Q8—91no—
264#121—91no—
265#121—91no—
266#120—181no—
267C4×D4—181no—
268C4×D4—181no—
269#117—91no—
270C2×C4⋊C4—61no—
271C2×C22⋊C4—61no—
272C22⋊C8—32no—
273C22⋊C8—61no—
274#95—32no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3(C2×D3)⋊C411yescharacteristic
291C23×C3(C2×D3)⋊C411yescharacteristic
292C23×C3(C2×D3)⋊C411yescharacteristic
293C23×C3(C2×D3)⋊C411yescharacteristic
294C23×C3C2×D1211yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—62no—
297C22×D3—61no—
298C22×D3—61no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—122no—
322C2×C3×C4—122no—
323C2×C3×C4—122no—
324C2×C3×C4(C2×D3)⋊C411yescharacteristic
325C2×C3×C4(C2×D3)⋊C411yescharacteristic
326C2×C3×C4(C2×D3)⋊C411yescharacteristic
327C2×C3×C4(C2×D3)⋊C411yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332#67—124no—
333#67—122no—
334#67—122no—
335#67—124no—
336#67—122no—
337#67—122no—
338#67—122no—
339#67—122no—
340#67—121no—
341#67—121no—
342#67—121no—
343#67—121no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356D12—121no—
357D12—121no—
358D12—122no—
359C4×D3—124no—
360C4×D3—122no—
361C4×D3—122no—
362Dic6—122no—
363Dic6—121no—
364Dic6—121no—
365C3×C8—122no—
366C3⋊C8—42no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—41no—
370C2×C32—41no—
371C2×C32C2×#9911yescharacteristic
372C2×C32#41711yescharacteristic
373C2×C32#42111yescharacteristic
374C3⋊D3—81no—
375C24#62611yescharacteristic
376#41—362no—
377C2×Q8—91no—
378C2×D4—91no—
379C2×D4—181no—
380C2×D4—181no—
381C2×D4—181no—
382C22×C4—42no—
383C22×C4—62no—
384C22×C4—181no—
385C22×C4#62411yescharacteristic
386C22×C4#62411yescharacteristic
387C22×C4#62611yescharacteristic
388C22×C4#62611yescharacteristic
389C22×C4#62611yescharacteristic
390C22×C4C2×D3211yescharacteristic
391M16—122no—
392C2×C8—62no—
393C4⋊C4—91no—
394C4⋊C4—91no—
395C4⋊C4—122no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—122no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—181no—
404C42—181no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3#90811yescharacteristic
439C22×C3#90911yescharacteristic
440C22×C3C2×(C2×D3)⋊C411yescharacteristic
441C22×C3C2×(C2×D3)⋊C411yescharacteristic
442C22×C3#93211yescharacteristic
443C22×C3#94211yescharacteristic
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C3×C4—22no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—242no—
464C3×C4#80612yes—
465C3×C4#80612yes—
466Dic3—82no—
467Dic3—122no—
468Dic3—122no—
469Dic3—122no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476C32#151311yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—41no—
480C23—41no—
481C23—181no—
482C23#372211yescharacteristic
483C23#372211yescharacteristic
484C23C2×#62611yescharacteristic
485Q8—361no—
486D4—361no—
487D4—362no—
488D4—362no—
489D4—361no—
490D4—361no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—122no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—362no—
504C2×C4#372211yescharacteristic
505C2×C4#372211yescharacteristic
506C2×C4C2×#62411yescharacteristic
507C2×C4C2×#62611yescharacteristic
508C8—122no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—41no—
517C2×C3—41no—
518C2×C3—42no—
519C2×C3—42no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3C2×#80611yescharacteristic
525C2×C3C2×#80611yescharacteristic
526C2×C3#496611yescharacteristic
527C2×C3#500511yescharacteristic
528C2×C3#513311yescharacteristic
529C2×C3#513911yescharacteristic
530D3—242no—
531D3—241no—
532D3—241no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—42no—
542C22—42no—
543C22—361no—
544C22—361no—
545C22—361no—
546C22#6383011yescharacteristic
547C22#6383311yescharacteristic
548C22C2×#372211yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—242no—
553C4—361no—
554C4—361no—
555C4—361no—
556C4#6358112yes—
557C3—21no—
558C3#6950811yescharacteristic, complemented
559C3#6997911yescharacteristic, complemented
560C2—21no—
561C2—21no—
562C2—41no—
563C2—41no—
564C2—721no—
565C2#1059110611yescharacteristic
566C2#1059111311yescharacteristic
567C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C3×#5207C2semidirect
4. #10589154C2semidirect
5. #10589151C2semidirect
9. C2×#3828C4semidirect
11. #64139C4semidirect
16. #64135C4semidirect
17. #64133C4semidirect
30. #5212D3semidirect
31. #5207D3semidirect
476. C32#1513semidirect
558. C3#69508semidirect
559. C3#69979semidirect

Maximal subgroups

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

subgroupindex
#105962622
C3×#52122
C3×#52072
#105891542
#105891512
#699793
#695083