Finite Group Databasebeta

← #11793946

Subgroups — #11793946

Order 1152.

603 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#951C211yesmaximal, characteristic
2#10592933C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63560C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72105—31nomaximal
9#70310—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#951—22no—
15C3×#951—22no—
16C2×C3×#216—21no—
17C2×C3×#214—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63657—22no—
22C3×#835—21no—
23C3×#832—21no—
24#63578—22no—
25#63565—22no—
26#63560—22no—
27C2×C3×#137—31no—
28C2×#951D311yescharacteristic
29C3×#417—31no—
30#5234—31no—
31#5234—31no—
32#5234—61no—
33#5232D311yescharacteristic
34C2×#836—31no—
35C2×#835—31no—
36C2×#824—31no—
37C2×#822—31no—
38C2×#822—31no—
39C2×#810—31no—
40#4554—31no—
41#4530—31no—
42C32×#41—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C2×C32×Q8D411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6D412yes—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×#216—24no—
66C3×#214—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2052—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×C3×Q8—31no—
80C22×Dic6C2×D311yescharacteristic
81C3×#137—62no—
82C3×#137—62no—
83C2×C3×Q16—61no—
84C2×C3×SD16—61no—
85C2×C3×M16—31no—
86C2×C3×M16—31no—
87C2×C3×C4⋊C4—31no—
88#951—22no—
89#951—22no—
90C2×#216—21no—
91C2×#214—21no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C3×#103—61no—
102C3×#102—61no—
103#836—62no—
104#835—21no—
105#835—62no—
106#832—21no—
107#830—62no—
108#830—62no—
109#830—64no—
110#824—62no—
111#822—62no—
112#822—62no—
113#810—62no—
114C23×C32—21no—
115C23×C32#4111yescharacteristic
116C32×Q8—21no—
117C32×Q8—21no—
118C32×D4—21no—
119C32×D4—21no—
120C32×D4—41no—
121C32×D4—41no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3×Dic3—22no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—81no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C3⋊(C3⋊C8)—22no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—41no—
144C2×#137—31no—
145C2×#108—91no—
146#417—31no—
147C2×#103—91no—
148C2×#101—91no—
149#408—91no—
150#343—91no—
151C3×#41—21no—
152C3×#41—21no—
153C3×#41—21no—
154C3×#41—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—41no—
160C3×#41—41no—
161C3×#41—41no—
162C3×#41—41no—
163C2×C3×Q8—21no—
164C2×C3×Q8—32no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8#6711yescharacteristic
171C2×C3×Q8#6711yescharacteristic
172C2×C3×D4—22no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4#6711yescharacteristic
177C2×C3×D4#6711yescharacteristic
178C22×C3×C4—22no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—21no—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—21no—
193C2×Dic6#6712yes—
194C3×Q16—64no—
195C3×SD16—64no—
196C3×M16—32no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204#216—24no—
205#214—24no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208#208—21no—
209#208—21no—
210#208—21no—
211#208—61no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—121no—
216#208—121no—
217#208#6712yes—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32#12111yescharacteristic
238C22×C32#12311yescharacteristic
239C22×C32#12411yescharacteristic
240C32×C4—41no—
241C32×C4#12011yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12311yescharacteristic
245C3×Dic3—42no—
246C3×Dic3—81no—
247C2×#41D3211yescharacteristic
248C22×Q8—31no—
249#137—62no—
250#137—62no—
251C2×Q16—61no—
252C2×SD16—61no—
253C2×M16—31no—
254C2×M16—31no—
255C2×M16—91no—
256C22×C8—91no—
257C2×C4⋊C4—31no—
258#108—182no—
259#103—61no—
260#103—182no—
261#102—61no—
262#101—182no—
263C22⋊C8—182no—
264C23×C3—22no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3#23711yescharacteristic
269C23×C3#23711yescharacteristic
270C3×Q8—21no—
271C3×Q8—21no—
272C3×Q8—21no—
273C3×Q8—21no—
274C3×Q8—41no—
275C3×Q8—41no—
276C3×Q8—62no—
277C3×Q8—62no—
278C3×Q8—121no—
279C3×Q8—121no—
280C3×D4—21no—
281C3×D4—21no—
282C3×D4—21no—
283C3×D4—21no—
284C3×D4—41no—
285C3×D4—41no—
286C3×D4—42no—
287C3×D4—42no—
288C3×D4—41no—
289C3×D4—41no—
290C3×D4—41no—
291C3×D4—41no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
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—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—241no—
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×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×Dic3—22no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—81no—
329Dic6—22no—
330Dic6—22no—
331Dic6—41no—
332Dic6—41no—
333C3×C8—62no—
334C3×C8—121no—
335C3⋊C8—22no—
336C3⋊C8—41no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—122no—
340C3⋊C8—122no—
341C3⋊C8—121no—
342C3⋊C8—121no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—81no—
346C2×C32#39411yescharacteristic
347C2×C32#47111yescharacteristic
348C2×C32#47311yescharacteristic
349#41—21no—
350#41—21no—
351#41—21no—
352#41—21no—
353C2×Q8—32no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8#62511yescharacteristic
360C2×D4—21no—
361C2×D4#62511yescharacteristic
362C22×C4—21no—
363C22×C4—61no—
364C22×C4—61no—
365C22×C4C2×D3211yescharacteristic
366Q16—64no—
367SD16—64no—
368M16—32no—
369M16—61no—
370M16—61no—
371M16—61no—
372M16—181no—
373M16—181no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—92no—
377C2×C8—181no—
378C2×C8—181no—
379C2×C8—181no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3#88311yescharacteristic
401C22×C3#88511yescharacteristic
402C22×C3#93511yescharacteristic
403C22×C3#93611yescharacteristic
404C22×C3#93911yescharacteristic
405C22×C3#93911yescharacteristic
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—42no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—122no—
414C3×C4—241no—
415C3×C4#88411yescharacteristic
416C3×C4#88411yescharacteristic
417C3×C4#92911yescharacteristic
418C3×C4#93511yescharacteristic
419C3×C4#93711yescharacteristic
420C3×C4#93811yescharacteristic
421C3×C4#93911yescharacteristic
422C3×C4#95311yescharacteristic
423Dic3—42no—
424Dic3—81no—
425C32#205211yescharacteristic, complemented, Sylow
426C23—21no—
427C23#380511yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—62no—
431Q8—62no—
432Q8—121no—
433Q8—121no—
434D4—21no—
435D4—21no—
436D4—41no—
437D4—41no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—62no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—121no—
445C2×C4—241no—
446C2×C4#380411yescharacteristic
447C2×C4#380411yescharacteristic
448C2×C4C2×#62511yescharacteristic
449C2×C4D3×#6711yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C2×C4#381111yescharacteristic
452C8—62no—
453C8—121no—
454C8—182no—
455C8—361no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—41no—
464C2×C3—41no—
465C2×C3—82no—
466C2×C3—81no—
467C2×C3—81no—
468C2×C3#495911yescharacteristic
469C2×C3#520011yescharacteristic
470C2×C3#520311yescharacteristic
471C2×C3#520411yescharacteristic
472C2×C3#520411yescharacteristic
473C2×C3#522211yescharacteristic
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#6395911yescharacteristic
480C22#6396911yescharacteristic
481C22#6398011yescharacteristic
482C4—41no—
483C4—122no—
484C4—241no—
485C4#6395811yescharacteristic
486C4#6396111yescharacteristic
487C4#6397111yescharacteristic
488C4#6397611yescharacteristic
489C3—21no—
490C3#7031011yescharacteristic, complemented
491C3#7210511yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—81no—
495C2#1059168111yescharacteristic
496C2#1059168311yescharacteristic
497C2#1059170811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
hypercenterC2×#41D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63578C2semidirect
5. C2×#63565C2semidirect
6. C2×#63560C2semidirect
7. #10589167C2semidirect
425. C32#2052semidirect
490. C3#70310semidirect
491. C3#72105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9512
#105929332
C3×#52322
C2×#635782
C2×#635652
C2×#635602
#105891672
#721053
#703103