Finite Group Databasebeta

← #11778641

Subgroups — #11778641

Order 1152.

504 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10594977C211yesmaximal, characteristic
2C3×#4674C211yesmaximal, characteristic, complemented
3#10591124C211yesmaximal, characteristic, complemented
4#10591089C211yesmaximal, characteristic, complemented
5#10589318C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69709—31nomaximal
9#68289—31nomaximal
10#64133C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15#63976—21no—
16Dic3×#67—21no—
17#63913—21no—
18#63891—21no—
19#63885—21no—
20#63858—21no—
21C32×#95C2211yescharacteristic
22#63657C2211yescharacteristic
23C3×C3⋊#95—21no—
24C3×#830C2211yescharacteristic
25#63576—21no—
26#63573—21no—
27#63567—21no—
28#63562—21no—
29#5617—31no—
30#5494—31no—
31C3×#397—31no—
32#5033—31no—
33#4971—31no—
34#4967—31no—
35#4721—31no—
36#4674D311yescharacteristic, complemented
37C3×#327—31no—
38#4525—31no—
39#4468—31no—
40#4452—31no—
41#4452—31no—
42#4452—61no—
43#4451D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#634D411yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×#625—21no—
53C2×#625—21no—
54C2×D3×Dic3—21no—
55#3757—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—42no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71Dic32—21no—
72#1612—91noSylow
73C3×#121—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×C3×C22⋊C4—61no—
77#953—61no—
78#939—61no—
79#937—61no—
80D4×Dic3—61no—
81#930C2×D311yescharacteristic
82C4×#67—61no—
83C2×(C2×D3)⋊C4—21no—
84C2×(C2×D3)⋊C4C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86#924—31no—
87#924—31no—
88#924—61no—
89#898—61no—
90#886—61no—
91#885—61no—
92#885—61no—
93#884—61no—
94#883—61no—
95#879—61no—
96C3×C22⋊C8—31no—
97C3×#95—21no—
98C3×#95—61no—
99C3×#95C2×D311yescharacteristic
100C3×#95C2×D311yescharacteristic
101#832—61no—
102C3⋊#95—21no—
103#830—31no—
104#830—31no—
105#830—61no—
106#830C2×D311yescharacteristic
107#817—61no—
108#816—61no—
109#810—61no—
110#809—61no—
111#808—61no—
112#807—61no—
113#807—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129#634—41no—
130C3×#67—41no—
131C3×#67—41no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×D12—41no—
139#625—81no—
140#625—81no—
141D3×Dic3—81no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—41no—
144#538—91no—
145#483—91no—
146#480—91no—
147#397—31no—
148#328—91no—
149#327—31no—
150#323—91no—
151C24×C3—31no—
152C23×D3#6711yescharacteristic
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—21no—
164C2×#67—61no—
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—61no—
168C22×Dic3—21no—
169C22×Dic3—61no—
170C22×Dic3#6711yescharacteristic
171C2×D12D1211yescharacteristic
172C2×C4×D3—61no—
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—122no—
184#217—61no—
185#217—61no—
186#217—61no—
187#217—61no—
188#217—61no—
189#217—121no—
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—42no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3D1211yescharacteristic
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—121no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—121no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3×D3—42no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—81no—
227C32×C4—21no—
228C32×C4—21no—
229C32×C4—81no—
230C3⋊Dic3—41no—
231C3⋊Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235#126—181no—
236#124—181no—
237#123—181no—
238C22⋊Q8—91no—
239#121—31no—
240#121—181no—
241#120—181no—
242C4×D4—181no—
243C2×C4⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—61no—
246#107—181no—
247#106—181no—
248#103—181no—
249#102—181no—
250C22⋊C8—31no—
251C22⋊C8—91no—
252#95—61no—
253#95D3211yescharacteristic
254C23×C3—21no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—61no—
258C23×C3—61no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3D3×D411yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—21no—
264C22×D3—21no—
265C22×D3—21no—
266C22×D3—21no—
267C22×D3—41no—
268C22×D3—41no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4—121no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—42no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—81no—
286C2×C3×C4—81no—
287C2×C3×C4—81no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296#67—41no—
297#67—41no—
298#67—241no—
299#67—241no—
300#67—241no—
301#67—241no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—241no—
315D12—41no—
316C4×D3—241no—
317Dic6—121no—
318Dic6—121no—
319Dic6—241no—
320C3×C8—121no—
321C3⋊C8—41no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C3⋊C8—241no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32#44911yescharacteristic
328C2×C32#45511yescharacteristic
329C2×C32#45811yescharacteristic
330C3×D3—81no—
331C3×D3—81no—
332C24—31no—
333C2×Q8—91no—
334C2×D4—31no—
335C2×D4—61no—
336C2×D4—181no—
337C2×D4—181no—
338C22×C4—21no—
339C22×C4—31no—
340C22×C4—61no—
341C22×C4—181no—
342C22×C4C2×D3211yescharacteristic
343C2×C8—61no—
344C2×C8—181no—
345C4⋊C4—31no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—91no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C22⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—122no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C42—181no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—122no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3—121no—
376C22×C3—241no—
377C22×C3#88211yescharacteristic
378C22×C3#91111yescharacteristic
379C22×C3#91611yescharacteristic
380C22×C3#93211yescharacteristic
381C22×C3#93711yescharacteristic
382C22×C3#95011yescharacteristic
383C2×D3—42no—
384C2×D3—41no—
385C2×D3—41no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C2×D3—81no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—81no—
398C3×C4—81no—
399C3×C4—82no—
400C3×C4—121no—
401C3×C4—121no—
402C3×C4—241no—
403Dic3—41no—
404Dic3—41no—
405Dic3—81no—
406Dic3—121no—
407Dic3—121no—
408Dic3—121no—
409Dic3—121no—
410Dic3—241no—
411Dic3—241no—
412C32#161211yescharacteristic, complemented, Sylow
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—121no—
418C23—121no—
419C23D3×#6711yescharacteristic
420Q8—361no—
421D4—121no—
422D4—121no—
423D4—121no—
424D4—721no—
425D4—721no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—181no—
437C2×C4—181no—
438C2×C4—721no—
439C2×C4D3×D1211yescharacteristic
440C2×C4#380211yescharacteristic
441C8—121no—
442C8—361no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—241no—
453C2×C3—241no—
454C2×C3#474211yescharacteristic
455C2×C3#478111yescharacteristic
456C2×C3#482511yescharacteristic
457C2×C3#503711yescharacteristic
458C2×C3#505311yescharacteristic
459C2×C3#506111yescharacteristic
460D3—81no—
461D3—81no—
462C22—21no—
463C22—21no—
464C22—122no—
465C22—121no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22—241no—
472C22#6392211yescharacteristic
473C22#6393211yescharacteristic
474C22#6394711yescharacteristic
475C4—21no—
476C4—21no—
477C4—81no—
478C4—121no—
479C4—121no—
480C4—241no—
481C4—361no—
482C4—361no—
483C3—21no—
484C3#6828911yescharacteristic, complemented
485C3#6970911yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—241no—
489C2—241no—
490C2#1059039611yescharacteristic
491C2#1059040811yescharacteristic
492C2#1059061311yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10594977C2
hypercenter#95D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4674C2semidirect
3. #10591124C2semidirect
4. #10591089C2semidirect
5. #10589318C2semidirect
6. C3×#4451C2semidirect
7. #10589145C2semidirect
36. #4674D3semidirect
43. #4451D3semidirect
412. C32#1612semidirect
484. C3#68289semidirect
485. C3#69709semidirect

Maximal subgroups

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

subgroupindex
#105949772
C3×#46742
#105911242
#105910892
#105893182
C3×#44512
#105891452
#697093
#682893