Finite Group Databasebeta

← #11793959

Subgroups — #11793959

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×#63833C211yesmaximal, characteristic
2#10592828C211yesmaximal, characteristic
3C2×C3×#824C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6C2×#63565C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#70126—31nomaximal
9#68987—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3719—21no—
18#63833—22no—
19#63833—22no—
20C2×#3717—21no—
21#63647—22no—
22C3×#824—22no—
23#63578—22no—
24#63567—21no—
25#63565—22no—
26#63564—21no—
27C2×#942—31no—
28C2×#909—31no—
29C2×C3×#101—31no—
30C2×#835—31no—
31C2×#824D311yescharacteristic, complemented
32#5133—31no—
33#5129—31no—
34#5129—31no—
35#5129—61no—
36C2×#822—31no—
37C2×#822—31no—
38C2×#810—31no—
39#4966—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634D411yescharacteristic
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—
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
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—21no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×#216—61no—
88#942—62no—
89#942—62no—
90C2×#215—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×#208C2×D311yescharacteristic
93C2×#208C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97#909—62no—
98#909—62no—
99C2×Dic12—61no—
100C2×#204—61no—
101C3×#101—62no—
102#835—62no—
103#824—22no—
104#822—62no—
105#822—62no—
106#821—61no—
107(C2×D3)⋊C8—62no—
108(C2×D3)⋊C8—62no—
109(C2×D3)⋊C8—64no—
110#816—61no—
111#810—61no—
112#810—62no—
113#809—61no—
114C23×C32#4111yescharacteristic
115C22×C3⋊D3—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122#638—41no—
123#638—41no—
124C2×C3⋊Dic3—21no—
125C4⋊(C3⋊D3)—21no—
126C4⋊(C3⋊D3)—21no—
127C4×C3⋊D3—41no—
128C4×C3⋊D3—41no—
129#634—21no—
130#634—21no—
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—
140C32×C8—41no—
141C3⋊(C3⋊C8)—22no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—41no—
144C2×#137—91no—
145C2×#108—91no—
146#417—91no—
147C2×#103—91no—
148C2×#101—31no—
149#408—91no—
150#343—31no—
151C2×C3×Q8—32no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—62no—
163C2×#67—61no—
164C2×#67—61no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—121no—
176#235—121no—
177#235—121no—
178#235—121no—
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—61no—
182C2×C4×D3—62no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—31no—
191C2×Dic6—31no—
192C2×Dic6—61no—
193C2×Dic6#6712yes—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—32no—
199C3×M16—41no—
200C3×M16—41no—
201C3×M16—61no—
202C3×M16—61no—
203C3×M16—61no—
204C2×C3×C8—22no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211#216—64no—
212#215—64no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208D1212yes—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8—121no—
230Dic12—64no—
231#204—64no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32#12111yescharacteristic
235C22×C32#12311yescharacteristic
236C22×C32#12411yescharacteristic
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C2×C3⋊D3—41no—
240C32×C4#12011yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—41no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C2×#41—91no—
248C22×Q8—31no—
249#137—182no—
250#137—182no—
251C2×Q16—181no—
252C2×SD16—181no—
253C2×M16—31no—
254C2×M16—31no—
255C2×M16D3211yescharacteristic
256C22×C8—91no—
257C2×C4⋊C4—31no—
258#108—182no—
259#103—181no—
260#103—182no—
261#102—181no—
262#101—62no—
263C22⋊C8—182no—
264C23×C3—21no—
265C23×C3#23511yescharacteristic
266C23×C3#23511yescharacteristic
267C22×D3—62no—
268C22×D3—61no—
269C22×D3—61no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×Q8—121no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—62no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—241no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4#23511yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23911yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—122no—
298#67—122no—
299#67—121no—
300#67—121no—
301#67—121no—
302#67—121no—
303C2×Dic3—22no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—81no—
311D12—61no—
312D12—61no—
313D12—61no—
314D12—61no—
315D12—121no—
316D12—121no—
317C4×D3—122no—
318C4×D3—122no—
319C4×D3—121no—
320C4×D3—121no—
321C4×D3—121no—
322C4×D3—121no—
323Dic6—22no—
324Dic6—22no—
325Dic6—41no—
326Dic6—41no—
327Dic6—61no—
328Dic6—61no—
329Dic6—61no—
330Dic6—61no—
331Dic6—121no—
332Dic6—121no—
333C3×C8—42no—
334C3×C8—41no—
335C3×C8—41no—
336C3×C8—62no—
337C3×C8—121no—
338C3⋊C8—22no—
339C3⋊C8—41no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—122no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#39411yescharacteristic
346C2×C32#47111yescharacteristic
347C2×C32#47311yescharacteristic
348C3⋊D3—81no—
349#41—181no—
350#41—181no—
351#41—181no—
352#41—181no—
353C2×Q8—32no—
354C2×Q8—61no—
355C2×Q8—61no—
356C2×Q8—61no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—91no—
360C2×D4—91no—
361C2×D4—181no—
362C22×C4—61no—
363C22×C4—61no—
364C22×C4—181no—
365C22×C4C2×D3211yescharacteristic
366Q16—184no—
367SD16—184no—
368M16—21no—
369M16—21no—
370M16—32no—
371M16—61no—
372M16—61no—
373M16—61no—
374C2×C8—21no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—92no—
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#87511yescharacteristic
392C22×C3#88411yescharacteristic
393C22×C3#88411yescharacteristic
394C22×C3#88511yescharacteristic
395C22×C3#89411yescharacteristic
396C22×C3#92911yescharacteristic
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—121no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—122no—
411C3×C4—241no—
412C3×C4#88211yescharacteristic
413C3×C4#88311yescharacteristic
414C3×C4#88411yescharacteristic
415C3×C4#88411yescharacteristic
416C3×C4#89411yescharacteristic
417C3×C4#89511yescharacteristic
418C3×C4#93711yescharacteristic
419C3×C4#93911yescharacteristic
420Dic3—42no—
421Dic3—81no—
422Dic3—122no—
423Dic3—121no—
424Dic3—121no—
425C32#205211yescharacteristic, complemented, Sylow
426C23—181no—
427C23#379811yescharacteristic
428Q8—62no—
429Q8—62no—
430Q8—121no—
431Q8—121no—
432Q8—181no—
433Q8—181no—
434D4—181no—
435D4—181no—
436D4—361no—
437D4—361no—
438C2×C4—62no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4—181no—
443C2×C4—241no—
444C2×C4—361no—
445C2×C4—361no—
446C2×C4#379911yescharacteristic
447C2×C4D3×D1211yescharacteristic
448C2×C4#380211yescharacteristic
449C2×C4#380411yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C2×C4#381111yescharacteristic
452C8—41no—
453C8—62no—
454C8—121no—
455C8—182no—
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#467211yescharacteristic
466C2×C3#474811yescharacteristic
467C2×C3#475411yescharacteristic
468C2×C3#475511yescharacteristic
469C2×C3#475511yescharacteristic
470C2×C3#495911yescharacteristic
471D3—242no—
472D3—241no—
473D3—241no—
474C22—21no—
475C22—21no—
476C22—361no—
477C22—361no—
478C22—361no—
479C22#6385011yescharacteristic
480C22#6385211yescharacteristic
481C22#6391211yescharacteristic
482C4—122no—
483C4—241no—
484C4—361no—
485C4#6385411yescharacteristic
486C4#6391011yescharacteristic
487C4#6392211yescharacteristic
488C4#6397111yescharacteristic
489C3—21no—
490C3#6898711yescharacteristic, complemented
491C3#7012611yescharacteristic, complemented
492C2—21no—
493C2—21no—
494C2—721no—
495C2#1059099111yescharacteristic
496C2#1059099311yescharacteristic
497C2#1059129211yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#3828C22
hypercenterC2×M16D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#824C2semidirect
4. C2×#63578C2semidirect
6. C2×#63565C2semidirect
7. C3×#4554C2semidirect
31. C2×#824D3semidirect
41. #4554D3semidirect
425. C32#2052semidirect
490. C3#68987semidirect
491. C3#70126semidirect

Maximal subgroups

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

subgroupindex
C2×#638332
#105928282
C2×C3×#8242
C2×#635782
#105911062
C2×#635652
C3×#45542
#701263
#689873