Finite Group Databasebeta

← #11778645

Subgroups — #11778645

Order 1152.

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

normal subgroups only

This group has 509 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#10595038C211yesmaximal, characteristic
2C3×#4721C211yesmaximal, characteristic, complemented
3#10591314C211yesmaximal, characteristic, complemented
4#10591133C211yesmaximal, characteristic, complemented
5#10589336C211yesmaximal, characteristic, complemented
6C3×#4468C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71173—31nomaximal
9#68111—31nomaximal
10#64139C2211yescharacteristic
11C2×C3×(C2×D3)⋊C4C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924C2211yescharacteristic
14#63977—21no—
15C2×(C2×D3)⋊Dic3—21no—
16#63952—21no—
17#63910—21no—
18#63907—21no—
19#63861—21no—
20#63854—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63658C2211yescharacteristic
23C3×#830C2211yescharacteristic
24C3×#817—21no—
25C3×#816—21no—
26#63579—21no—
27#63575—21no—
28#63564—21no—
29#5644—31no—
30#5494—31no—
31C3×#483—31no—
32#4992—31no—
33#4967—31no—
34#4953—31no—
35#4736—31no—
36#4721D311yescharacteristic, complemented
37C3×#323—31no—
38#4538—31no—
39#4470—31no—
40#4470—31no—
41#4470—61no—
42#4468D311yescharacteristic, complemented
43#4467—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#626—21no—
53C2×#626—21no—
54C2×#624—21no—
55C2×C32×C8—21no—
56#3752—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3722—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—42no—
71Dic32—21no—
72#1612—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76#953—61no—
77C2×#217—61no—
78#947—61no—
79#930—31no—
80#930—31no—
81#930—61no—
82C4×#67—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86#924C2×D311yescharacteristic
87#898—61no—
88#895—61no—
89#894—61no—
90#885—61no—
91#884—61no—
92#883—61no—
93#882—61no—
94#67⋊C4—61no—
95#879—61no—
96C3×#106—61no—
97C3×#103—61no—
98C3×C22⋊C8—21no—
99C3×C22⋊C8—31no—
100C3×C22⋊C8C2×D311yescharacteristic
101C3×C22⋊C8C2×D311yescharacteristic
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107#830C2×D311yescharacteristic
108#821—61no—
109#818—61no—
110#817—21no—
111#816—21no—
112#809—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×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124#638—41no—
125#638—41no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C4⋊(C3⋊D3)—41no—
131C2×C3×Dic3—21no—
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×Dic6—41no—
139#626—81no—
140#626—81no—
141#624—81no—
142C32×C8—41no—
143C3×C3⋊C8—41no—
144#538—91no—
145#483—31no—
146#480—91no—
147#397—91no—
148#328—91no—
149#327—91no—
150#323—31no—
151C24×C3—31no—
152C23×D3D1211yescharacteristic
153C2×C3×Q8—31no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—61no—
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—121no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3D1211yescharacteristic
169C2×D12—31no—
170C2×D12—31no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×Dic6#6711yescharacteristic
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—41no—
180C2×C3×C8—61no—
181C3×C4⋊C4—31no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188#217—21no—
189#217—61no—
190#217—61no—
191#217—122no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198(C2×D3)⋊C4—61no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—121no—
201(C2×D3)⋊C4—122no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—31no—
205C4⋊Dic3—31no—
206C4⋊Dic3—61no—
207C4⋊Dic3#6711yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C2×C3⋊C8—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3⋊D3—41no—
220C2×C3⋊D3—41no—
221C2×C3⋊D3—41no—
222C2×C3×D3—42no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—81no—
227C32×C4—21no—
228C32×C4—21no—
229C3⋊Dic3—41no—
230C3⋊Dic3—81no—
231C3×Dic3—41no—
232C3×Dic3—41no—
233C3×Dic3—41no—
234C3×Dic3—81no—
235#126—181no—
236#124—181no—
237#123—181no—
238C22⋊Q8—31no—
239#121—91no—
240#121—181no—
241#120—181no—
242C4×D4—181no—
243C2×C4⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—181no—
246#107—181no—
247#106—61no—
248#103—61no—
249#102—181no—
250C22⋊C8—31no—
251C22⋊C8D3211yescharacteristic
252#95—91no—
253#95—181no—
254C23×C3—21no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—61no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3C2×D1211yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—21no—
263C22×D3—21no—
264C22×D3—21no—
265C22×D3—41no—
266C22×D3—41no—
267C22×D3—61no—
268C22×D3—61no—
269C22×D3—121no—
270C3×Q8—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—81no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287#67—121no—
288#67—121no—
289#67—121no—
290#67—121no—
291#67—241no—
292#67—241no—
293#67—241no—
294#67—241no—
295C2×Dic3—21no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—41no—
301C2×Dic3—41no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—122no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—241no—
313C2×Dic3—241no—
314D12—121no—
315D12—121no—
316D12—241no—
317D12—241no—
318D12—241no—
319C4×D3—241no—
320C4×D3—241no—
321Dic6—41no—
322C3×C8—41no—
323C3×C8—41no—
324C3×C8—81no—
325C3×C8—121no—
326C3⋊C8—41no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32#44911yescharacteristic
330C2×C32#45511yescharacteristic
331C2×C32#45811yescharacteristic
332C3⋊D3—81no—
333C3×D3—81no—
334C24—31no—
335C2×Q8—31no—
336C2×D4—91no—
337C2×D4—181no—
338C2×D4—181no—
339C2×D4—181no—
340C22×C4—31no—
341C22×C4—61no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—21no—
346C2×C8—61no—
347C4⋊C4—31no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4—91no—
352C4⋊C4—181no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C22⋊C4—362no—
361C42—181no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—122no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3—241no—
376C22×C3#88211yescharacteristic
377C22×C3#90411yescharacteristic
378C22×C3#90811yescharacteristic
379C22×C3#91411yescharacteristic
380C22×C3#91611yescharacteristic
381C22×C3#93711yescharacteristic
382C2×D3—42no—
383C2×D3—41no—
384C2×D3—41no—
385C2×D3—41no—
386C2×D3—81no—
387C2×D3—121no—
388C2×D3—121no—
389C2×D3—121no—
390C2×D3—121no—
391C2×D3—121no—
392C2×D3—121no—
393C2×D3—241no—
394C2×D3—241no—
395C2×D3—241no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—121no—
405C3×C4—241no—
406Dic3—41no—
407Dic3—41no—
408Dic3—41no—
409Dic3—81no—
410Dic3—121no—
411Dic3—121no—
412Dic3—241no—
413Dic3—241no—
414Dic3—241no—
415Dic3—242no—
416C32#161211yescharacteristic, complemented, Sylow
417C23—61no—
418C23—61no—
419C23—61no—
420C23—121no—
421C23—121no—
422C23—181no—
423C23D3×D1211yescharacteristic
424Q8—121no—
425D4—361no—
426D4—361no—
427D4—361no—
428D4—721no—
429D4—721no—
430C2×C4—41no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—121no—
435C2×C4—121no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—181no—
439C2×C4—361no—
440C2×C4—361no—
441C2×C4—361no—
442C2×C4—721no—
443C2×C4#380211yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C8—41no—
446C8—121no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—41no—
455C2×C3—41no—
456C2×C3—241no—
457C2×C3#473411yescharacteristic
458C2×C3#474211yescharacteristic
459C2×C3#474611yescharacteristic
460C2×C3#505311yescharacteristic
461C2×C3#517211yescharacteristic
462C2×C3#520211yescharacteristic
463D3—81no—
464D3—241no—
465D3—241no—
466D3—481no—
467C22—21no—
468C22—21no—
469C22—122no—
470C22—121no—
471C22—121no—
472C22—121no—
473C22—241no—
474C22—361no—
475C22—361no—
476C22—361no—
477C22#6379411yescharacteristic
478C22#6380611yescharacteristic
479C22#6392211yescharacteristic
480C4—21no—
481C4—21no—
482C4—121no—
483C4—121no—
484C4—121no—
485C4—241no—
486C4—361no—
487C4—721no—
488C3—21no—
489C3#6811111yescharacteristic, complemented
490C3#7117311yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—241no—
494C2—721no—
495C2#1059040811yescharacteristic
496C2#1059082311yescharacteristic
497C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10595038C2
hypercenterC22⋊C8D32
hypocenterC32#1612
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4721C2semidirect
3. #10591314C2semidirect
4. #10591133C2semidirect
5. #10589336C2semidirect
6. C3×#4468C2semidirect
7. #10589152C2semidirect
36. #4721D3semidirect
42. #4468D3semidirect
416. C32#1612semidirect
489. C3#68111semidirect
490. C3#71173semidirect

Maximal subgroups

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

subgroupindex
#105950382
C3×#47212
#105913142
#105911332
#105893362
C3×#44682
#105891522
#711733
#681113