Finite Group Databasebeta

← #11794542

Subgroups — #11794542

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63648C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4#10591212C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4551C211yesmaximal, characteristic, complemented
8#70484—31nomaximal
9#68901—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3724—21no—
18C2×#3722—21no—
19C2×#3722—21no—
20#63648—22no—
21C3×Dic3⋊C8—22no—
22#63579—21no—
23#63575—22no—
24#63564—22no—
25C2×C3×C4⋊C8—31no—
26C2×#821—31no—
27C2×#821—31no—
28C2×#821—31no—
29C2×#821—61no—
30C2×#818—31no—
31C2×Dic3⋊C8D311yescharacteristic, complemented
32#4988—31no—
33#4972—31no—
34C2×#809—31no—
35C2×#807—31no—
36#4939—31no—
37#4928—31no—
38C3×#340—31no—
39#4551D311yescharacteristic, complemented
40C23×C3⋊D3—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)Q812yes—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3D411yescharacteristic
52C22×C3×Dic3D411yescharacteristic
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D412yes—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8D412yes—
67#3724—42no—
68#3722—42no—
69#3722—42no—
70#2067—91noSylow
71C22×D12—31no—
72C22×D12—31no—
73C22×D12—61no—
74C22×C3×C8—21no—
75C22×C3×C8—31no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C42—31no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×Dic3⋊C4—61no—
91C2×Dic3⋊C4—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94C3×C4⋊C8—62no—
95C3⋊#95—61no—
96C3⋊#95—61no—
97#821—62no—
98#821—62no—
99#821—62no—
100#821—64no—
101#818—62no—
102Dic3⋊C8—22no—
103#809—62no—
104#807—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×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×Q811yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—41no—
125C4⋊(C3⋊D3)—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3D812yes—
138C32×C8—41no—
139C3×C3⋊C8—22no—
140C2×#107—91no—
141C2×C4⋊C8—31no—
142C2×#102—91no—
143C2×#102—91no—
144#390—91no—
145#389—91no—
146#340—31no—
147C23×D3—61no—
148C23×D3—61no—
149C23×D3—121no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—121no—
162C22×Dic3D1211yescharacteristic
163C22×Dic3D1211yescharacteristic
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—62no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—121no—
180C2×D12—121no—
181C2×D12—121no—
182C2×C3×C8—22no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—32no—
190C2×C3×C8—41no—
191C2×C3×C8—41no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—61no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C42—61no—
199C3×C42—61no—
200(C2×D3)⋊C4—122no—
201(C2×D3)⋊C4—122no—
202(C2×D3)⋊C4—122no—
203(C2×D3)⋊C4—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—62no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—121no—
214Dic3⋊C4—122no—
215Dic3⋊C4—122no—
216C4×Dic3—21no—
217C4×Dic3—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8#6712yes—
221C22×C32#12111yescharacteristic
222C22×C32#12111yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C22×C32C2×D811yescharacteristic
225C22×C32#13511yescharacteristic
226C22×C32AGL(1,ℤ/8)11yescharacteristic
227C22×C32#13711yescharacteristic
228C2×C3⋊D3—42no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—81no—
232C2×C3⋊D3—81no—
233C2×C3⋊D3—81no—
234C2×C3⋊D3—81no—
235C32×C4#12111yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4C22⋊Q811yescharacteristic
238C32×C4#12611yescharacteristic
239C3⋊Dic3—42no—
240C3×Dic3—22no—
241C3×Dic3—41no—
242C3×Dic3—81no—
243C3×Dic3—81no—
244C22×D4—91no—
245C22×C8—31no—
246C22×C8D3211yescharacteristic
247C2×C4⋊C4—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—181no—
251C2×C22⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C42—31no—
254#107—182no—
255C4⋊C8—62no—
256#102—182no—
257#102—182no—
258#95—181no—
259C23×C3—21no—
260C23×C3C2×D1211yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—62no—
263C22×D3—62no—
264C22×D3—122no—
265C22×D3—122no—
266C22×D3—122no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—121no—
270C22×D3—121no—
271C22×D3—121no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—121no—
278C22×D3—121no—
279C22×D3—241no—
280C22×D3—241no—
281C22×D3—241no—
282C22×D3—241no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—32no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
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×C4#23711yescharacteristic
309C2×C3×C4D3×Q811yescharacteristic
310C2×C3×C4D3×Q811yescharacteristic
311C2×C3×C4#23911yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—122no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—241no—
332C2×Dic3—241no—
333C2×Dic3D2412yes—
334D12—64no—
335D12—62no—
336D12—62no—
337D12—62no—
338D12—62no—
339D12—122no—
340D12—122no—
341D12—122no—
342D12—121no—
343D12—121no—
344D12—121no—
345D12—121no—
346C3×C8—42no—
347C3×C8—41no—
348C3×C8—41no—
349C3×C8—62no—
350C3⋊C8—22no—
351C2×C32#39611yescharacteristic
352C2×C32#45911yescharacteristic
353C2×C32#46411yescharacteristic
354C2×C32#46611yescharacteristic
355C2×C32#46811yescharacteristic
356C2×C32#47411yescharacteristic
357C2×C32#47811yescharacteristic
358C3⋊D3—82no—
359C24—181no—
360C2×D4—92no—
361C2×D4—181no—
362C2×D4—181no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—181no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—181no—
371C22×C4C2×D3211yescharacteristic
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—32no—
376C2×C8—61no—
377C2×C8—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—92no—
383C4⋊C4—181no—
384C4⋊C4—362no—
385C22⋊C4—362no—
386C22⋊C4—362no—
387C42—61no—
388C42—61no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3#88411yescharacteristic
397C22×C3#88411yescharacteristic
398C22×C3#89511yescharacteristic
399C22×C3#89611yescharacteristic
400C22×C3#89711yescharacteristic
401C22×C3C2×D2411yescharacteristic
402C22×C3#90411yescharacteristic
403C22×C3#90811yescharacteristic
404C22×C3#90911yescharacteristic
405C22×C3D3×D811yescharacteristic
406C22×C3#91411yescharacteristic
407C22×C3#91611yescharacteristic
408C22×C3#91811yescharacteristic
409C22×C3#93011yescharacteristic
410C2×D3—124no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—122no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—242no—
420C2×D3—242no—
421C2×D3—242no—
422C2×D3—242no—
423C2×D3—241no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—241no—
427C2×D3—241no—
428C2×D3—241no—
429C2×D3—241no—
430C2×D3—241no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—62no—
436C3×C4—121no—
437C3×C4—241no—
438C3×C4—241no—
439C3×C4#87611yescharacteristic
440C3×C4#88411yescharacteristic
441C3×C4#89611yescharacteristic
442C3×C4#89611yescharacteristic
443C3×C4#89611yescharacteristic
444C3×C4#89811yescharacteristic
445C3×C4#93911yescharacteristic
446C3×C4#94611yescharacteristic
447Dic3—22no—
448Dic3—41no—
449Dic3—81no—
450Dic3—81no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454C32#206711yescharacteristic, complemented, Sylow
455C23—182no—
456C23—361no—
457C23—361no—
458C23—361no—
459C23—361no—
460C23—361no—
461C23—361no—
462C23D3×D1211yescharacteristic
463D4—182no—
464D4—182no—
465D4—361no—
466D4—361no—
467C2×C4—32no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—182no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C4#379711yescharacteristic
483C2×C4#379811yescharacteristic
484C2×C4#379911yescharacteristic
485C2×C4#380411yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4#381111yescharacteristic
488C8—41no—
489C8—62no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3#467611yescharacteristic
498C2×C3#477511yescharacteristic
499C2×C3#478611yescharacteristic
500C2×C3#479811yescharacteristic
501C2×C3#481211yescharacteristic
502C2×C3#484311yescharacteristic
503C2×C3#484511yescharacteristic
504C2×C3#484611yescharacteristic
505C2×C3#484711yescharacteristic
506C2×C3#487111yescharacteristic
507C2×C3#489011yescharacteristic
508C2×C3#499411yescharacteristic
509C2×C3#511511yescharacteristic
510C2×C3#513411yescharacteristic
511D3—244no—
512D3—242no—
513D3—242no—
514C22—362no—
515C22—362no—
516C22—362no—
517C22—721no—
518C22—721no—
519C22—721no—
520C22—721no—
521C22D3×D2411yescharacteristic
522C22#6379411yescharacteristic
523C22#6380111yescharacteristic
524C22#6380611yescharacteristic
525C22#6389511yescharacteristic
526C22#6390611yescharacteristic
527C22#6391011yescharacteristic
528C4—62no—
529C4—121no—
530C4—241no—
531C4—241no—
532C4—362no—
533C4#6386511yescharacteristic
534C4#6386811yescharacteristic
535C4#6388811yescharacteristic
536C4#6397111yescharacteristic
537C3—21no—
538C3#6890111yescharacteristic, complemented
539C3#7048411yescharacteristic, complemented
540C2—722no—
541C2#1059076411yescharacteristic
542C2#1059076511yescharacteristic
543C2#1059076911yescharacteristic
544C2#1059081311yescharacteristic
545C2#1059082611yescharacteristic
546C2#1059085011yescharacteristic
547C2#1059134711yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2067
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C8C2semidirect
4. #10591212C2semidirect
5. C2×#63575C2semidirect
7. C3×#4551C2semidirect
31. C2×Dic3⋊C8D3semidirect
39. #4551D3semidirect
454. C32#2067semidirect
538. C3#68901semidirect
539. C3#70484semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C2×C3×Dic3⋊C82
#105913202
#105912122
C2×#635752
C2×#635642
C3×#45512
#704843
#689013