Finite Group Databasebeta

← #11793960

Subgroups — #11793960

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63831C211yesmaximal, characteristic
2C2×#63651C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6#10591087C211yesmaximal, characteristic
7C3×#4554C211yesmaximal, characteristic, complemented
8#70004—31nomaximal
9#68987—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3719—21no—
18#63831—22no—
19#63831—22no—
20C2×#3716—21no—
21#63651—22no—
22C3×(C2×D3)⋊C8—22no—
23#63577—22no—
24#63567—22no—
25#63565—21no—
26#63562—21no—
27C2×#951—31no—
28C2×#909—31no—
29C3×#408—31no—
30#5232—31no—
31C2×#824—31no—
32C2×#824—31no—
33C2×#824—61no—
34#5129D311yescharacteristic
35C2×#822—31no—
36C2×#819—31no—
37C2×#816—31no—
38C2×#810—31no—
39#4966—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634D412yes—
50C2×C3×#67—21no—
51C22×C3×Dic3—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×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×#208—21no—
68C3×#208D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3719—24no—
74#3716—24no—
75#2052—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C22×Dic6—31no—
79C22×Dic6—31no—
80C22×Dic6—61no—
81C2×C3×M16—21no—
82C2×C3×M16—31no—
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×M16C2×D311yescharacteristic
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—31no—
87#951—62no—
88#951—62no—
89C2×#216—61no—
90C2×#214—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#909—62no—
98#909—62no—
99C2×Dic12—61no—
100C2×#204—61no—
101C3×C22⋊C8—62no—
102#835—61no—
103#832—61no—
104#824—62no—
105#824—62no—
106#824—64no—
107#822—62no—
108(C2×D3)⋊C8—22no—
109#819—62no—
110#816—62no—
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
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125#634—22no—
126#634—22no—
127#634—41no—
128#634—41no—
129C3×#67—41no—
130C3×#67—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—81no—
134C3×D12—21no—
135C3×D12—21no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6—21no—
140C32×C8—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C2×#137—91no—
145C2×#108—91no—
146#417—91no—
147C2×#103—91no—
148C2×#101—91no—
149#408—31no—
150#343—31no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—31no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—21no—
164C22×Dic3—21no—
165C22×Dic3—62no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168#235—21no—
169#235—21no—
170#235—21no—
171#235—21no—
172C2×D12D1211yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6—32no—
175C2×Dic6—32no—
176C2×Dic6—62no—
177C2×Dic6—61no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—62no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—121no—
189C2×Dic6—121no—
190C2×Dic6—121no—
191C2×Dic6—121no—
192C2×Dic6D1211yescharacteristic
193C3×M16—22no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—32no—
199C3×M16—41no—
200C3×M16—61no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—32no—
204C2×C3×C8—41no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210#216—64no—
211#214—64no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214#208—21no—
215#208—62no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—121no—
221#208D1212yes—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—121no—
228C2×C3⋊C8#6712yes—
229Dic12—64no—
230#204—64no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32#12111yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#12411yescharacteristic
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4#12011yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12311yescharacteristic
243C3⋊Dic3—42no—
244C3×Dic3—41no—
245C3×Dic3—81no—
246C2×#41—31no—
247C22×Q8—91no—
248#137—182no—
249#137—182no—
250C2×Q16—181no—
251C2×SD16—181no—
252C2×M16—31no—
253C2×M16—91no—
254C2×M16D3211yescharacteristic
255C22×C8—31no—
256C2×C4⋊C4—31no—
257#108—182no—
258#103—182no—
259#103—181no—
260#102—181no—
261#101—182no—
262C22⋊C8—62no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23511yescharacteristic
267C22×D3—21no—
268C3×Q8—61no—
269C3×Q8—61no—
270C3×D4—61no—
271C3×D4—61no—
272C3×D4—121no—
273C3×D4—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—61no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—241no—
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4C2×D1211yescharacteristic
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×C4#23711yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23911yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297#67—41no—
298#67—41no—
299C2×Dic3—21no—
300C2×Dic3—41no—
301C2×Dic3—64no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—81no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311D12—21no—
312D12—21no—
313C4×D3—41no—
314C4×D3—41no—
315Dic6—21no—
316Dic6—21no—
317Dic6—62no—
318Dic6—62no—
319Dic6—62no—
320Dic6—62no—
321Dic6—122no—
322Dic6—122no—
323Dic6—122no—
324Dic6—122no—
325Dic6—121no—
326Dic6—121no—
327Dic6—121no—
328Dic6—121no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3×C8—62no—
333C3×C8—62no—
334C3⋊C8—22no—
335C3⋊C8—22no—
336C3⋊C8—122no—
337C3⋊C8—121no—
338C3⋊C8—121no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#39411yescharacteristic
342C2×C32#47111yescharacteristic
343C2×C32#47311yescharacteristic
344C3×D3—81no—
345#41—61no—
346#41—61no—
347#41—61no—
348#41—61no—
349C2×Q8—31no—
350C2×Q8—92no—
351C2×Q8—181no—
352C2×Q8—181no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×D4—31no—
357C2×D4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—181no—
361C22×C4C2×D3211yescharacteristic
362Q16—184no—
363SD16—184no—
364M16—21no—
365M16—21no—
366M16—32no—
367M16—61no—
368M16—181no—
369M16—181no—
370C2×C8—21no—
371C2×C8—32no—
372C2×C8—61no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—181no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—121no—
390C22×C3#87511yescharacteristic
391C22×C3#88311yescharacteristic
392C22×C3#88411yescharacteristic
393C22×C3#88511yescharacteristic
394C22×C3#89411yescharacteristic
395C22×C3#93011yescharacteristic
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—121no—
404C3×C4—241no—
405C3×C4#88211yescharacteristic
406C3×C4#88211yescharacteristic
407C3×C4#88411yescharacteristic
408C3×C4#88611yescharacteristic
409C3×C4#89411yescharacteristic
410C3×C4#89511yescharacteristic
411C3×C4#93811yescharacteristic
412C3×C4#93911yescharacteristic
413Dic3—41no—
414Dic3—81no—
415Dic3—124no—
416Dic3—122no—
417Dic3—122no—
418C32#205211yescharacteristic, complemented, Sylow
419C23—61no—
420C23#379811yescharacteristic
421Q8—61no—
422Q8—61no—
423Q8—182no—
424Q8—182no—
425Q8—361no—
426Q8—361no—
427D4—61no—
428D4—61no—
429D4—121no—
430D4—121no—
431C2×C4—61no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—121no—
435C2×C4—182no—
436C2×C4—241no—
437C2×C4—361no—
438C2×C4—361no—
439C2×C4#379611yescharacteristic
440C2×C4D3×D1211yescharacteristic
441C2×C4D3×D1211yescharacteristic
442C2×C4#380411yescharacteristic
443C2×C4D3×#6711yescharacteristic
444C2×C4#381111yescharacteristic
445C8—41no—
446C8—62no—
447C8—62no—
448C8—361no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—41no—
457C2×C3—41no—
458C2×C3—241no—
459C2×C3#467211yescharacteristic
460C2×C3#474811yescharacteristic
461C2×C3#475511yescharacteristic
462C2×C3#496111yescharacteristic
463C2×C3#514111yescharacteristic
464C2×C3#514311yescharacteristic
465D3—81no—
466C22—21no—
467C22—21no—
468C22—121no—
469C22—121no—
470C22—121no—
471C22#6385211yescharacteristic
472C22#6385311yescharacteristic
473C22#6390611yescharacteristic
474C4—121no—
475C4—241no—
476C4—362no—
477C4#6388611yescharacteristic
478C4#6389011yescharacteristic
479C4#6392311yescharacteristic
480C4#6395811yescharacteristic
481C3—21no—
482C3#6898711yescharacteristic, complemented
483C3#7000411yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—241no—
487C2#1059099611yescharacteristic
488C2#1059099911yescharacteristic
489C2#1059131211yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
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
2. C2×#63651C2semidirect
4. C2×#63577C2semidirect
5. C2×#63567C2semidirect
7. C3×#4554C2semidirect
41. #4554D3semidirect
418. C32#2052semidirect
482. C3#68987semidirect
483. C3#70004semidirect

Maximal subgroups

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

subgroupindex
C2×#638312
C2×#636512
C3×#51292
C2×#635772
C2×#635672
#105910872
C3×#45542
#700043
#689873