Finite Group Databasebeta

← #11794538

Subgroups — #11794538

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63634C211yesmaximal, characteristic, complemented
2C3×#4988C211yesmaximal, characteristic
3#10591212C211yesmaximal, characteristic, complemented
4C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C2×#63562C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#69653—31nomaximal
9#68901—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724—21no—
20#63634—22no—
21#63579—21no—
22Dic3⋊(C3⋊C8)—22no—
23#63563—22no—
24#63562—22no—
25C3×#390—31no—
26C2×#832—31no—
27C2×#832—31no—
28C2×#821—31no—
29C2×Dic3⋊C8—31no—
30#4988D311yescharacteristic
31#4972—31no—
32C2×#809—31no—
33C2×#807—31no—
34C2×#807—31no—
35C2×#807—61no—
36#4928—31no—
37C2×C4⋊(C3⋊C8)—31no—
38C3×#340—31no—
39#4529D311yescharacteristic, complemented
40C23×C3×D3—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3D411yescharacteristic
46C22×C3×Dic3D411yescharacteristic
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12Q812yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)D412yes—
60C3×(C2×D3)⋊C4—42no—
61C3×(C2×D3)⋊C4—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4×Dic3—21no—
65C3×C4×Dic3—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#3724—42no—
70#2067—91noSylow
71C22×C3×D4—31no—
72C22×D12C2×D311yescharacteristic
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×C3×C22⋊C4—61no—
79C2×C3×C22⋊C4—61no—
80C2×C3×C42—31no—
81C2×(C2×D3)⋊C4—21no—
82C2×(C2×D3)⋊C4—21no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89C2×C4×Dic3C2×D311yescharacteristic
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94#832—62no—
95#832—62no—
96C3⋊#95—61no—
97C3⋊#95—61no—
98#821—62no—
99Dic3⋊C8—62no—
100#809—62no—
101#807—62no—
102#807—62no—
103#807—64no—
104C4⋊(C3⋊C8)—62no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C22×C3×D3—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×Q811yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3D812yes—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C3⋊(C3⋊C8)—22no—
139C3×C3⋊C8—41no—
140C2×#107—91no—
141C2×C4⋊C8—91no—
142C2×#102—91no—
143C2×#102—91no—
144#390—31no—
145#389—91no—
146#340—31no—
147C24×C3—61no—
148C23×D3—21no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—41no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C22×D311yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3#6711yescharacteristic
169C22×Dic3#6711yescharacteristic
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12Dic612yes—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—122no—
188C3×C22⋊C4—122no—
189C3×C42—61no—
190C3×C42—61no—
191(C2×D3)⋊C4—42no—
192(C2×D3)⋊C4—42no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—32no—
196C4⋊Dic3—32no—
197C4⋊Dic3—62no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—121no—
201Dic3⋊C4—122no—
202Dic3⋊C4—122no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—32no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C22×C32#12111yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32C22⋊Q811yescharacteristic
220C22×C32C2×D811yescharacteristic
221C22×C32#13511yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C22×C32#13711yescharacteristic
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C32×C4—81no—
232C32×C4#12111yescharacteristic
233C32×C4C22⋊Q811yescharacteristic
234C32×C4C22⋊Q811yescharacteristic
235C32×C4#12611yescharacteristic
236C3⋊Dic3—42no—
237C3×Dic3—22no—
238C3×Dic3—41no—
239C3×Dic3—81no—
240C22×D4—31no—
241C22×C8—31no—
242C22×C8—91no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4D3211yescharacteristic
247C2×C22⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C42—31no—
250#107—182no—
251C4⋊C8—182no—
252#102—182no—
253#102—182no—
254#95—181no—
255C23×C3—21no—
256C23×C3—62no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3D3×D411yescharacteristic
264C23×C3C2×#6711yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—121no—
275C3×D4—121no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—32no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4C2×Dic611yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4D3×Q811yescharacteristic
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—241no—
328C2×Dic3—241no—
329C2×Dic3#21312yes—
330D12—22no—
331D12—22no—
332D12—41no—
333D12—41no—
334C3×C8—121no—
335C3⋊C8—41no—
336C3⋊C8—64no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C2×C32#39611yescharacteristic
340C2×C32#45911yescharacteristic
341C2×C32#46411yescharacteristic
342C2×C32#46611yescharacteristic
343C2×C32#46811yescharacteristic
344C2×C32#47411yescharacteristic
345C2×C32#47811yescharacteristic
346C3×D3—82no—
347C24—61no—
348C2×D4—32no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C22×C4—21no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—61no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—92no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—92no—
371C4⋊C4—181no—
372C4⋊C4—362no—
373C22⋊C4—122no—
374C22⋊C4—122no—
375C42—61no—
376C42—61no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3—122no—
387C22×C3—241no—
388C22×C3—241no—
389C22×C3—241no—
390C22×C3—241no—
391C22×C3#88411yescharacteristic
392C22×C3#88411yescharacteristic
393C22×C3#89611yescharacteristic
394C22×C3D3×D811yescharacteristic
395C22×C3#91411yescharacteristic
396C22×C3#91611yescharacteristic
397C22×C3#91811yescharacteristic
398C22×C3#92411yescharacteristic
399C22×C3C2×#21311yescharacteristic
400C22×C3#93211yescharacteristic
401C22×C3#93811yescharacteristic
402C22×C3#93911yescharacteristic
403C22×C3#95011yescharacteristic
404C22×C3#95111yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—81no—
409C2×D3—81no—
410C2×D3—81no—
411C2×D3—81no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—62no—
417C3×C4—82no—
418C3×C4—81no—
419C3×C4—81no—
420C3×C4—121no—
421C3×C4—241no—
422C3×C4#87611yescharacteristic
423C3×C4#87811yescharacteristic
424C3×C4#87811yescharacteristic
425C3×C4#87911yescharacteristic
426C3×C4#88411yescharacteristic
427C3×C4#88411yescharacteristic
428C3×C4#89611yescharacteristic
429C3×C4#89611yescharacteristic
430Dic3—22no—
431Dic3—41no—
432Dic3—81no—
433Dic3—122no—
434Dic3—122no—
435Dic3—242no—
436C32#206711yescharacteristic, complemented, Sylow
437C23—62no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23—121no—
442C23—121no—
443C23—121no—
444C23D3×#6711yescharacteristic
445D4—62no—
446D4—62no—
447D4—121no—
448D4—121no—
449C2×C4—32no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—182no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4D3×Dic611yescharacteristic
465C2×C4#379511yescharacteristic
466C2×C4#379811yescharacteristic
467C2×C4#380211yescharacteristic
468C2×C4#380411yescharacteristic
469C2×C4#381111yescharacteristic
470C8—121no—
471C8—182no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—242no—
480C2×C3#467611yescharacteristic
481C2×C3#477511yescharacteristic
482C2×C3#478611yescharacteristic
483C2×C3#479811yescharacteristic
484C2×C3#481211yescharacteristic
485C2×C3#487111yescharacteristic
486C2×C3#489011yescharacteristic
487C2×C3#494811yescharacteristic
488C2×C3#500711yescharacteristic
489C2×C3#500911yescharacteristic
490C2×C3#503811yescharacteristic
491C2×C3#504211yescharacteristic
492C2×C3#505411yescharacteristic
493C2×C3#507211yescharacteristic
494D3—82no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22—241no—
499C22—241no—
500C22—241no—
501C22—241no—
502C22#6385111yescharacteristic
503C22#6388511yescharacteristic
504C22D3×#21311yescharacteristic
505C22#6393411yescharacteristic
506C22#6394311yescharacteristic
507C22#6394711yescharacteristic
508C22#6395811yescharacteristic
509C4—62no—
510C4—81no—
511C4—121no—
512C4—241no—
513C4—362no—
514C4#6385911yescharacteristic
515C4#6389611yescharacteristic
516C4#6389911yescharacteristic
517C4#6391211yescharacteristic
518C3—21no—
519C3#6890111yescharacteristic, complemented
520C3#6965311yescharacteristic, complemented
521C2—242no—
522C2#1059049911yescharacteristic
523C2#1059051511yescharacteristic
524C2#1059054511yescharacteristic
525C2#1059055511yescharacteristic
526C2#1059130911yescharacteristic
527C2#1059142911yescharacteristic
528C2#1059157711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2067
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63634C2semidirect
3. #10591212C2semidirect
4. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C3×#4529C2semidirect
39. #4529D3semidirect
436. C32#2067semidirect
519. C3#68901semidirect
520. C3#69653semidirect

Maximal subgroups

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

subgroupindex
C2×#636342
C3×#49882
#105912122
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#635622
C3×#45292
#696533
#689013