Finite Group Databasebeta

← #11793908

Subgroups — #11793908

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63825C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic, complemented
3C3×#4966C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7C3×#4530C211yesmaximal, characteristic, complemented
8#70307—31nomaximal
9#68986—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3717—21no—
18#63825—22no—
19#63825—22no—
20C2×#3714—21no—
21#63636—22no—
22C3×#810—21no—
23C3×#809—21no—
24#63578—22no—
25#63559—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×#949—31no—
28C2×#908—31no—
29C3×#417—31no—
30#5234—31no—
31C2×#823—31no—
32C2×#823—31no—
33#5129—31no—
34C2×#822—31no—
35C2×#822—31no—
36#4966D311yescharacteristic, complemented
37C2×#809—31no—
38C2×#809—31no—
39C2×#809—61no—
40C3×#343—31no—
41#4530D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)D412yes—
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208D412yes—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3717—24no—
74#3714—24no—
75#2051—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C22×D12—31no—
79C22×D12—31no—
80C22×D12—61no—
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87#949—62no—
88#949—62no—
89C2×#215—61no—
90C2×#213—61no—
91C2×#208C2×D311yescharacteristic
92C2×#208C2×D311yescharacteristic
93C2×#208C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97#908—62no—
98#908—62no—
99C2×D24—61no—
100C2×#204—61no—
101C3×#103—61no—
102C3×#102—61no—
103#830—62no—
104#823—62no—
105#823—62no—
106#822—62no—
107#822—62no—
108(C2×D3)⋊C8—62no—
109#810—21no—
110#809—21no—
111#809—62no—
112#809—62no—
113#809—64no—
114C23×C32#4111yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3⋊D3—41no—
117C22×C3⋊D3—41no—
118C22×C3⋊D3—81no—
119C22×C3⋊D3—81no—
120C22×C3×D3—21no—
121C2×C32×C4—41no—
122C2×C32×C4—81no—
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—41no—
132C4⋊(C3⋊D3)—41no—
133C3×#67—41no—
134C3×#67—41no—
135C2×C3×Dic3—21no—
136C3×D12—21no—
137C3×D12—21no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C3⋊(C3⋊C8)—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—91no—
147C2×#108—91no—
148#417—31no—
149C2×#102—91no—
150C2×#100—91no—
151#408—91no—
152#343—31no—
153C23×D3—61no—
154C23×D3—61no—
155C23×D3—121no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C3×#41—61no—
160C2×C3×Q8—31no—
161C2×C3×D4—31no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—41no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174#235—21no—
175C2×D12—32no—
176C2×D12—32no—
177C2×D12—62no—
178C2×D12—62no—
179C2×D12—62no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—121no—
191C2×D12—121no—
192C2×D12—121no—
193C2×D12#6711yescharacteristic
194C2×C4×D3—21no—
195C2×Dic6#6711yescharacteristic
196C3×M16—32no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—41no—
211#215—64no—
212#213—64no—
213#208—21no—
214#208—21no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208D1212yes—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8—121no—
231D24—64no—
232#204—64no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12111yescharacteristic
236C22×C32#12311yescharacteristic
237C22×C32#12411yescharacteristic
238C2×C3⋊D3—42no—
239C2×C3⋊D3—82no—
240C2×C3⋊D3—81no—
241C2×C3⋊D3—81no—
242C2×C3⋊D3—82no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—81no—
247C32×C4#12011yescharacteristic
248C32×C4#12111yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12311yescharacteristic
251C3×Dic3—41no—
252C2×#41—31no—
253C22×D4—91no—
254AGL(1,ℤ/8)—182no—
255AGL(1,ℤ/8)—182no—
256C2×SD16—181no—
257C2×D8—181no—
258C2×M16—31no—
259C2×M16—31no—
260C2×M16—31no—
261C22×C8—91no—
262C2×C4⋊C4D3211yescharacteristic
263#108—182no—
264#103—61no—
265#102—61no—
266#102—182no—
267#100—182no—
268C22⋊C8—182no—
269C23×C3—21no—
270C23×C3—61no—
271C23×C3#23511yescharacteristic
272C23×C3#23711yescharacteristic
273C22×D3—21no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—121no—
280C22×D3—121no—
281C22×D3—121no—
282C22×D3—121no—
283C22×D3—242no—
284C22×D3—242no—
285C22×D3—241no—
286C22×D3—241no—
287C22×D3—241no—
288C22×D3—241no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×D4—61no—
292C3×D4—61no—
293C3×D4—121no—
294C3×D4—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—61no—
305C2×C3×C4—82no—
306C2×C3×C4—81no—
307C2×C3×C4—81no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4C2×D1211yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23911yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322#67—41no—
323#67—41no—
324C2×Dic3—21no—
325D12—21no—
326D12—21no—
327D12—64no—
328D12—62no—
329D12—62no—
330D12—62no—
331D12—62no—
332D12—122no—
333D12—122no—
334D12—122no—
335D12—121no—
336D12—121no—
337D12—121no—
338D12—121no—
339C4×D3—41no—
340C4×D3—41no—
341Dic6—21no—
342Dic6—21no—
343C3×C8—62no—
344C3×C8—121no—
345C3×C8—121no—
346C3⋊C8—22no—
347C3⋊C8—41no—
348C3⋊C8—41no—
349C3⋊C8—62no—
350C3⋊C8—62no—
351C3⋊C8—122no—
352C2×C32—21no—
353C2×C32—21no—
354C2×C32#39411yescharacteristic
355C2×C32#47111yescharacteristic
356C2×C32#47211yescharacteristic
357C3⋊D3—82no—
358C3×D3—81no—
359C24—181no—
360#41—61no—
361#41—61no—
362#41—61no—
363#41—61no—
364C2×Q8—31no—
365C2×D4—31no—
366C2×D4—61no—
367C2×D4—92no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—181no—
373C22×C4—21no—
374C22×C4—61no—
375C22×C4C2×D3211yescharacteristic
376SD16—184no—
377D8—184no—
378M16—32no—
379M16—61no—
380M16—61no—
381M16—61no—
382M16—61no—
383M16—61no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—92no—
388C2×C8—181no—
389C2×C8—181no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3—121no—
404C22×C3#87511yescharacteristic
405C22×C3#88311yescharacteristic
406C22×C3#88411yescharacteristic
407C22×C3#88511yescharacteristic
408C22×C3#89411yescharacteristic
409C22×C3#93911yescharacteristic
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—124no—
414C2×D3—122no—
415C2×D3—122no—
416C2×D3—244no—
417C2×D3—244no—
418C2×D3—242no—
419C2×D3—242no—
420C2×D3—242no—
421C2×D3—242no—
422C2×D3—241no—
423C2×D3—241no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—242no—
427C2×D3—242no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—82no—
433C3×C4—81no—
434C3×C4—81no—
435C3×C4—121no—
436C3×C4#88211yescharacteristic
437C3×C4#88411yescharacteristic
438C3×C4#88411yescharacteristic
439C3×C4#88411yescharacteristic
440C3×C4#89411yescharacteristic
441C3×C4#89511yescharacteristic
442C3×C4#92911yescharacteristic
443C3×C4#93711yescharacteristic
444Dic3—41no—
445C32#205111yescharacteristic, complemented, Sylow
446C23—61no—
447C23—182no—
448C23—361no—
449C23—361no—
450C23—721no—
451C23—721no—
452C23#380411yescharacteristic
453Q8—61no—
454Q8—61no—
455D4—61no—
456D4—61no—
457D4—121no—
458D4—121no—
459D4—182no—
460D4—182no—
461D4—361no—
462D4—361no—
463C2×C4—41no—
464C2×C4—61no—
465C2×C4—81no—
466C2×C4—121no—
467C2×C4—121no—
468C2×C4#379811yescharacteristic
469C2×C4#379911yescharacteristic
470C2×C4D3×D1211yescharacteristic
471C2×C4#380211yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C2×C4#381111yescharacteristic
474C8—62no—
475C8—121no—
476C8—121no—
477C8—182no—
478C2×C3—22no—
479C2×C3—22no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—241no—
488C2×C3#467211yescharacteristic
489C2×C3#474911yescharacteristic
490C2×C3#475411yescharacteristic
491C2×C3#495911yescharacteristic
492C2×C3#519911yescharacteristic
493C2×C3#520311yescharacteristic
494D3—81no—
495D3—244no—
496D3—242no—
497D3—242no—
498C22—21no—
499C22—21no—
500C22—121no—
501C22—121no—
502C22—121no—
503C22—362no—
504C22—722no—
505C22—722no—
506C22—721no—
507C22—721no—
508C22#6385211yescharacteristic
509C22#6385411yescharacteristic
510C22#6397111yescharacteristic
511C4—81no—
512C4—121no—
513C4#6385011yescharacteristic
514C4#6391011yescharacteristic
515C4#6391211yescharacteristic
516C4#6392211yescharacteristic
517C3—21no—
518C3#6898611yescharacteristic, complemented
519C3#7030711yescharacteristic, complemented
520C2—21no—
521C2—21no—
522C2—241no—
523C2—722no—
524C2#1059129211yescharacteristic
525C2#1059150811yescharacteristic
526C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#63825C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63636C2semidirect
3. C3×#4966C2semidirect
4. C2×#63578C2semidirect
5. C2×#63559C2semidirect
6. #10591071C2semidirect
7. C3×#4530C2semidirect
36. #4966D3semidirect
41. #4530D3semidirect
445. C32#2051semidirect
518. C3#68986semidirect
519. C3#70307semidirect

Maximal subgroups

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

subgroupindex
C2×#638252
C2×#636362
C3×#49662
C2×#635782
C2×#635592
#105910712
C3×#45302
#703073
#689863