Finite Group Databasebeta

← #11778067

Subgroups — #11778067

Order 1152.

589 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 589 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5602C211yesmaximal, characteristic, complemented
2C3×#5036C211yesmaximal, characteristic
3#10591300C211yesmaximal, characteristic, complemented
4#10591169C211yesmaximal, characteristic, complemented
5#10589403C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71888—31nomaximal
9#70970—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#121C2211yescharacteristic
12C3×#935—21no—
13C3×#935—21no—
14C3×D4×Dic3—21no—
15C2×C3×#213—21no—
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×#3715—21no—
24#63658C2211yescharacteristic
25#63657C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#809—21no—
28#63562—21no—
29C3×#539—31no—
30#5602D311yescharacteristic, complemented
31C3×#447—31no—
32#5222—31no—
33#5218—31no—
34#5046—31no—
35#5036D311yescharacteristic
36#4991—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4528—31no—
42#4469—31no—
43#4467—31no—
44C23×C3×D3—21no—
45C2×C32×D4—21no—
46C2×C32×D4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—42no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#213—42no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—42no—
74(C2×D3)⋊Dic3—42no—
75#3715—42no—
76#1597—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×D8—61no—
80C3×#126—61no—
81C3×#125—61no—
82C3×#123—61no—
83C3×#123—61no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×#121—21no—
87C3×#121C2×D311yescharacteristic
88C3×#121C2×D311yescharacteristic
89C3×C4×D4—61no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×#217—61no—
93C2×#215—61no—
94#935—21no—
95#935—21no—
96D4×Dic3—21no—
97C2×#214—61no—
98C2×#213—21no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101#924C2×D311yescharacteristic
102C2×Dic3⋊C4C2×D311yescharacteristic
103#889—21no—
104#879—21no—
105#878—21no—
106C3×#102—61no—
107C3×C22⋊C8—31no—
108#832—61no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—61no—
112#830—31no—
113#830—31no—
114#830—61no—
115#830C2×D311yescharacteristic
116#809—21no—
117#809—61no—
118C23×C32—21no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C32×D4—41no—
128C32×D4—41no—
129C32×D4—41no—
130C2×C32×C4—21no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—81no—
145C3×D12—22no—
146C3×D12—22no—
147C3×D12—41no—
148C3×D12—41no—
149C3×Dic6—41no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152#539—31no—
153#450—91no—
154#447—31no—
155#394—91no—
156#328—91no—
157#327—91no—
158#324—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—31no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—41no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—122no—
169C2×C3×D4#6711yescharacteristic
170C2×C3×D4#6711yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—121no—
181C22×Dic3#6711yescharacteristic
182C22×Dic3#6711yescharacteristic
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—42no—
186C2×Dic6#6711yescharacteristic
187C3×D8—122no—
188C2×C3×C8—61no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4#6711yescharacteristic
198C3×C4⋊C4#6711yescharacteristic
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—41no—
202C3×C22⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C42—61no—
207#217—21no—
208#217—21no—
209#217—21no—
210#217—21no—
211#217—122no—
212#217—122no—
213#215—122no—
214#214—122no—
215#213—42no—
216(C2×D3)⋊C4—122no—
217(C2×D3)⋊C4—122no—
218C4⋊Dic3—21no—
219C4⋊Dic3#6711yescharacteristic
220Dic3⋊C4—21no—
221Dic3⋊C4—21no—
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225C4×Dic3—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—81no—
242C2×C3×D3—81no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C32×C4—21no—
246C32×C4—21no—
247C32×C4—41no—
248C3⋊Dic3—81no—
249C3×Dic3—41no—
250C3×Dic3—41no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C22×D4—31no—
254C2×SD16—181no—
255C2×D8—61no—
256#126—61no—
257#125—61no—
258#123—61no—
259#123—61no—
260C22⋊Q8—31no—
261C22⋊Q8—61no—
262#121D3211yescharacteristic
263C4×D4—61no—
264C2×C4⋊C4—31no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4—181no—
267#102—61no—
268#102—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—91no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—41no—
276C23×C3—62no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3D3×D411yescharacteristic
284C23×C3C2×#6711yescharacteristic
285C22×D3—22no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—41no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3—41no—
292C3×Q8—121no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—81no—
302C3×D4—81no—
303C3×D4—81no—
304C3×D4—121no—
305C3×D4—121no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—241no—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×Dic3—21no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—41no—
333C2×Dic3—81no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—122no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—241no—
342C2×Dic3—241no—
343D12—22no—
344D12—22no—
345D12—41no—
346D12—41no—
347Dic6—41no—
348C3×C8—121no—
349C3⋊C8—41no—
350C3⋊C8—121no—
351C3⋊C8—121no—
352C3⋊C8—241no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—81no—
356C2×C32#44911yescharacteristic
357C2×C32#45411yescharacteristic
358C2×C32B(4,𝔽2)11yescharacteristic
359C3×D3—82no—
360C24—61no—
361C2×Q8—31no—
362C2×D4—21no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—122no—
366C2×D4#62511yescharacteristic
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—61no—
370C22×C4—181no—
371C22×C4C2×D3211yescharacteristic
372SD16—362no—
373D8—122no—
374C2×C8—61no—
375C2×C8—181no—
376C4⋊C4—31no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4#62511yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—362no—
390C22⋊C4—362no—
391C42—61no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—241no—
414C22×C3—241no—
415C22×C3—241no—
416C22×C3—241no—
417C22×C3#91111yescharacteristic
418C22×C3#91211yescharacteristic
419C22×C3#93711yescharacteristic
420C22×C3#94911yescharacteristic
421C22×C3#95011yescharacteristic
422C22×C3#95311yescharacteristic
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—81no—
427C2×D3—81no—
428C2×D3—81no—
429C2×D3—81no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—81no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—121no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446Dic3—41no—
447Dic3—241no—
448Dic3—241no—
449Dic3—242no—
450C32#159711yescharacteristic, complemented, Sylow
451C23—21no—
452C23—62no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23—121no—
459C23D3×#6711yescharacteristic
460Q8—121no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—62no—
465D4—62no—
466D4—121no—
467D4—121no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—241no—
478C2×C4—361no—
479C2×C4—361no—
480C2×C4—361no—
481C2×C4C2×#62511yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C8—121no—
484C8—361no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—81no—
495C2×C3—81no—
496C2×C3—161no—
497C2×C3—242no—
498C2×C3#503211yescharacteristic
499C2×C3#515811yescharacteristic
500C2×C3#520111yescharacteristic
501C2×C3#523811yescharacteristic
502C2×C3#524411yescharacteristic
503C2×C3#524511yescharacteristic
504D3—82no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—241no—
514C22—241no—
515C22—241no—
516C22—241no—
517C22#6392511yescharacteristic
518C22#6393311yescharacteristic
519C22#6397611yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—121no—
524C4—121no—
525C4—121no—
526C4—121no—
527C4—721no—
528C3—21no—
529C3#7097011yescharacteristic, complemented
530C3#7188811yescharacteristic, complemented
531C2—21no—
532C2—21no—
533C2—81no—
534C2—242no—
535C2#1059145011yescharacteristic
536C2#1059153011yescharacteristic
537C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5036C2
hypercenter#121D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5602C2semidirect
3. #10591300C2semidirect
4. #10591169C2semidirect
5. #10589403C2semidirect
6. #10589152C2semidirect
7. #10589147C2semidirect
30. #5602D3semidirect
450. C32#1597semidirect
529. C3#70970semidirect
530. C3#71888semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
C3×#50362
#105913002
#105911692
#105894032
#105891522
#105891472
#718883
#709703