Finite Group Databasebeta

← #11793957

Subgroups — #11793957

Order 1152.

605 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63833C211yesmaximal, characteristic
2#10592665C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic
7C3×#4530C211yesmaximal, characteristic, complemented
8#70264—31nomaximal
9#68987—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3719—21no—
18#63833—22no—
19#63833—22no—
20C2×#3717—21no—
21#63637—21no—
22#63636—21no—
23C3×#810—22no—
24#63577—22no—
25#63560—22no—
26#63557—22no—
27C2×#942—31no—
28C2×#909—31no—
29C2×C3×#103—31no—
30C2×#836—31no—
31C2×#824—31no—
32#5129—31no—
33C2×#822—31no—
34#5110—31no—
35C2×#819—31no—
36C2×#810D311yescharacteristic, complemented
37#4966—31no—
38#4966—31no—
39#4966—61no—
40C3×#343—31no—
41#4530D311yescharacteristic, complemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634D411yescharacteristic
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—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208D412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3719—24no—
74#3717—24no—
75#2052—91noSylow
76C22×C3×Q8—31no—
77C2×#235—31no—
78C2×#235—31no—
79C2×#235—61no—
80C22×Dic6C2×D311yescharacteristic
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#216—61no—
88#942—62no—
89#942—62no—
90C2×#215—61no—
91C2×#208—31no—
92C2×#208—31no—
93C2×#208—61no—
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#909—62no—
98#909—62no—
99C2×Dic12—61no—
100C2×#204—61no—
101C3×#103—62no—
102#836—62no—
103#824—62no—
104#822—62no—
105(C2×D3)⋊C8—62no—
106(C2×D3)⋊C8—62no—
107#819—62no—
108#810—22no—
109#810—61no—
110#810—61no—
111#810—62no—
112#809—61no—
113#809—61no—
114#809—62no—
115C23×C32#4111yescharacteristic
116C22×C3⋊D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4—81no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—41no—
126#638—41no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—21no—
130C4×C3⋊D3—41no—
131C4×C3⋊D3—41no—
132#634—21no—
133#634—21no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C2×#137—91no—
146C2×#108—91no—
147#417—91no—
148C2×#103—31no—
149C2×#101—91no—
150#408—91no—
151#343—31no—
152C2×C3×Q8—32no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—61no—
166C2×#67—61no—
167C2×#67—121no—
168C22×Dic3—21no—
169#235—62no—
170#235—62no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—121no—
180#235—121no—
181C2×D12—31no—
182C2×D12—31no—
183C2×D12—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—121no—
187C2×Dic6—21no—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6—21no—
192C2×Dic6—31no—
193C2×Dic6—31no—
194C2×Dic6—61no—
195C2×Dic6D1212yes—
196C3×M16—32no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C2×C3×C8—32no—
201C2×C3×C8—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#216—64no—
212#215—64no—
213#208—21no—
214#208—21no—
215#208—21no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—121no—
221#208—121no—
222#208D1212yes—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8#6712yes—
231Dic12—64no—
232#204—64no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12111yescharacteristic
236C22×C32#12311yescharacteristic
237C22×C32#12411yescharacteristic
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—41no—
241C32×C4—81no—
242C32×C4#12011yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12311yescharacteristic
246C3⋊Dic3—41no—
247C3×Dic3—42no—
248C2×#41—91no—
249C22×Q8—31no—
250#137—182no—
251#137—182no—
252C2×Q16—181no—
253C2×SD16—181no—
254C2×M16—31no—
255C2×M16—31no—
256C2×M16—91no—
257C22×C8—31no—
258C2×C4⋊C4D3211yescharacteristic
259#108—182no—
260#103—62no—
261#103—181no—
262#102—181no—
263#101—182no—
264C22⋊C8—182no—
265C23×C3—21no—
266C23×C3#23511yescharacteristic
267C23×C3#23711yescharacteristic
268C22×D3—61no—
269C22×D3—61no—
270C22×D3—121no—
271C3×Q8—62no—
272C3×Q8—62no—
273C3×Q8—121no—
274C3×Q8—121no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—62no—
285C2×C3×C4—82no—
286C2×C3×C4—81no—
287C2×C3×C4—81no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23911yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—122no—
303#67—122no—
304#67—121no—
305#67—121no—
306#67—121no—
307#67—121no—
308C2×Dic3—22no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—121no—
314D12—62no—
315D12—61no—
316D12—61no—
317D12—61no—
318D12—61no—
319D12—121no—
320C4×D3—122no—
321C4×D3—122no—
322C4×D3—121no—
323C4×D3—121no—
324C4×D3—121no—
325C4×D3—121no—
326Dic6—22no—
327Dic6—22no—
328Dic6—41no—
329Dic6—41no—
330Dic6—62no—
331Dic6—61no—
332Dic6—61no—
333Dic6—61no—
334Dic6—61no—
335Dic6—121no—
336C3×C8—62no—
337C3×C8—62no—
338C3×C8—121no—
339C3⋊C8—22no—
340C3⋊C8—22no—
341C3⋊C8—41no—
342C3⋊C8—122no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32#39411yescharacteristic
348C2×C32#47111yescharacteristic
349C2×C32#47311yescharacteristic
350C3⋊D3—81no—
351#41—181no—
352#41—181no—
353#41—181no—
354#41—181no—
355C2×Q8—32no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×Q8—91no—
362C2×D4—91no—
363C2×D4—181no—
364C22×C4—21no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368Q16—184no—
369SD16—184no—
370M16—32no—
371M16—61no—
372M16—61no—
373M16—61no—
374M16—181no—
375M16—181no—
376C2×C8—32no—
377C2×C8—61no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8—181no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3#87511yescharacteristic
394C22×C3#88411yescharacteristic
395C22×C3#88511yescharacteristic
396C22×C3#88611yescharacteristic
397C22×C3#89411yescharacteristic
398C22×C3#93811yescharacteristic
399C2×D3—122no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C2×D3—241no—
407C2×D3—241no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—82no—
413C3×C4—81no—
414C3×C4—81no—
415C3×C4—122no—
416C3×C4#88211yescharacteristic
417C3×C4#88211yescharacteristic
418C3×C4#88311yescharacteristic
419C3×C4#88411yescharacteristic
420C3×C4#89411yescharacteristic
421C3×C4#89511yescharacteristic
422C3×C4#93011yescharacteristic
423C3×C4#93911yescharacteristic
424Dic3—42no—
425Dic3—122no—
426Dic3—121no—
427Dic3—121no—
428C32#205211yescharacteristic, complemented, Sylow
429C23—181no—
430C23#380411yescharacteristic
431Q8—62no—
432Q8—62no—
433Q8—121no—
434Q8—121no—
435Q8—181no—
436Q8—181no—
437D4—181no—
438D4—181no—
439D4—361no—
440D4—361no—
441C2×C4—41no—
442C2×C4—62no—
443C2×C4—81no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—181no—
447C2×C4—361no—
448C2×C4—361no—
449C2×C4#379611yescharacteristic
450C2×C4#379811yescharacteristic
451C2×C4D3×D1211yescharacteristic
452C2×C4D3×D1211yescharacteristic
453C2×C4D3×#6711yescharacteristic
454C2×C4#381111yescharacteristic
455C8—62no—
456C8—62no—
457C8—121no—
458C8—361no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3#467211yescharacteristic
469C2×C3#474811yescharacteristic
470C2×C3#475511yescharacteristic
471C2×C3#496111yescharacteristic
472C2×C3#517711yescharacteristic
473C2×C3#519211yescharacteristic
474D3—242no—
475D3—241no—
476D3—241no—
477C22—21no—
478C22—21no—
479C22—361no—
480C22—361no—
481C22—361no—
482C22#6385211yescharacteristic
483C22#6389011yescharacteristic
484C22#6395811yescharacteristic
485C4—81no—
486C4—122no—
487C4—361no—
488C4#6385311yescharacteristic
489C4#6388611yescharacteristic
490C4#6390611yescharacteristic
491C4#6392311yescharacteristic
492C3—21no—
493C3#6898711yescharacteristic, complemented
494C3#7026411yescharacteristic, complemented
495C2—21no—
496C2—21no—
497C2—721no—
498C2#1059131211yescharacteristic
499C2#1059140711yescharacteristic
500C2#1059154311yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2052
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
3. C2×C3×#810C2semidirect
4. C2×#63577C2semidirect
5. C2×#63560C2semidirect
7. C3×#4530C2semidirect
36. C2×#810D3semidirect
41. #4530D3semidirect
428. C32#2052semidirect
493. C3#68987semidirect
494. C3#70264semidirect

Maximal subgroups

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

subgroupindex
C2×#638332
#105926652
C2×C3×#8102
C2×#635772
C2×#635602
#105910732
C3×#45302
#702643
#689873