Finite Group Databasebeta

← #11793958

Subgroups — #11793958

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63827C211yesmaximal, characteristic
2C2×C3×#810C211yesmaximal, characteristic, complemented
3C3×#4966C211yesmaximal, characteristic
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic
7#10589396C211yesmaximal, characteristic, complemented
8#70310—31nomaximal
9#70264—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3718—21no—
18#63827—22no—
19#63827—22no—
20C2×#3715—21no—
21C3×#810—21no—
22C3×#810—22no—
23C3×#809—21no—
24#63577—22no—
25#63560—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×#951—31no—
28C2×#942—31no—
29C3×#417—31no—
30C2×C3×#103—31no—
31#5234—31no—
32C2×#836—31no—
33C2×#824—31no—
34C2×#822—31no—
35#5110—31no—
36C2×#819—31no—
37C2×#810D311yescharacteristic, complemented
38#4966D311yescharacteristic
39#4530—31no—
40#4530—31no—
41#4530—61no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6D412yes—
58C2×C3×Dic6D411yescharacteristic
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61#3748—21no—
62#3748—21no—
63#3748—21no—
64#3748D412yes—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#208—21no—
68C3×#208—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3718—24no—
74#3715—24no—
75#2052—91noSylow
76C2×C3×#41—31no—
77C22×C3×Q8—31no—
78C2×#235C2×D311yescharacteristic
79C22×Dic6C2×D311yescharacteristic
80C2×C3×M16—31no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85#951—62no—
86#951—62no—
87C2×#216—61no—
88C2×#216—61no—
89#942—62no—
90#942—62no—
91C2×#215—61no—
92C2×#214—61no—
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208—61no—
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C3×#103—62no—
102C3×#103—61no—
103C3×#102—61no—
104#836—62no—
105#830—62no—
106#824—62no—
107#822—62no—
108(C2×D3)⋊C8—62no—
109#819—62no—
110#810—21no—
111#810—22no—
112#809—21no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4—81no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C3×#67—41no—
124C3×#67—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C3×D12—21no—
130C3×D12—21no—
131C3×C4×D3—41no—
132C3×C4×D3—41no—
133C3×Dic6—22no—
134C3×Dic6—21no—
135C3×Dic6—22no—
136C3×Dic6—21no—
137C3×Dic6—41no—
138C3×Dic6—41no—
139C3⋊(C3⋊C8)—22no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C2×#137—91no—
144C2×#108—91no—
145#417—31no—
146C2×#103—31no—
147C2×#101—91no—
148#408—91no—
149#343—91no—
150C3×#41—61no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C2×C3×Q8—32no—
155C2×C3×Q8—31no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C2×C3×Q8—61no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×D4—31no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—21no—
172C22×Dic3—21no—
173#235—21no—
174#235—21no—
175#235—21no—
176#235—21no—
177C2×D12#6711yescharacteristic
178C2×C4×D3—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6D1212yes—
185C2×Dic6#6711yescharacteristic
186C3×M16—61no—
187C3×M16—61no—
188C2×C3×C8—32no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4—41no—
198#216—64no—
199#216—64no—
200#215—64no—
201#214—64no—
202#208—21no—
203#208—21no—
204#208—32no—
205#208—32no—
206#208—62no—
207#208—61no—
208#208—61no—
209#208—62no—
210#208—61no—
211#208—61no—
212#208—61no—
213#208—61no—
214#208—121no—
215#208—121no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8#6712yes—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32#12111yescharacteristic
229C22×C32#12311yescharacteristic
230C22×C32#12411yescharacteristic
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—81no—
235C32×C4#12011yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12111yescharacteristic
238C32×C4#12311yescharacteristic
239C3×Dic3—42no—
240C3×Dic3—41no—
241C2×#41—31no—
242C22×Q8—31no—
243#137—182no—
244#137—182no—
245C2×Q16—181no—
246C2×SD16—181no—
247C2×M16—31no—
248C2×M16—91no—
249C2×M16—91no—
250C22×C8—31no—
251C2×C4⋊C4D3211yescharacteristic
252#108—182no—
253#103—62no—
254#103—61no—
255#102—61no—
256#101—182no—
257C22⋊C8—182no—
258C23×C3—21no—
259C23×C3—61no—
260C23×C3#23711yescharacteristic
261C23×C3#23711yescharacteristic
262C22×D3—21no—
263C3×Q8—61no—
264C3×Q8—61no—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—121no—
268C3×Q8—121no—
269C3×D4—61no—
270C3×D4—61no—
271C3×D4—121no—
272C3×D4—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—62no—
283C2×C3×C4—61no—
284C2×C3×C4—81no—
285C2×C3×C4—81no—
286C2×C3×C4—82no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—41no—
304#67—41no—
305C2×Dic3—22no—
306C2×Dic3—21no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309D12—21no—
310D12—21no—
311C4×D3—41no—
312C4×D3—41no—
313Dic6—22no—
314Dic6—21no—
315Dic6—22no—
316Dic6—21no—
317Dic6—41no—
318Dic6—41no—
319C3×C8—62no—
320C3×C8—121no—
321C3⋊C8—22no—
322C3⋊C8—41no—
323C3⋊C8—62no—
324C3⋊C8—62no—
325C3⋊C8—122no—
326C3⋊C8—122no—
327C3⋊C8—121no—
328C3⋊C8—121no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32#39411yescharacteristic
332C2×C32#47111yescharacteristic
333C2×C32#47311yescharacteristic
334C3×D3—81no—
335#41—61no—
336#41—61no—
337#41—61no—
338#41—61no—
339C2×Q8—32no—
340C2×Q8—31no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—31no—
347C2×D4—61no—
348C22×C4—21no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4C2×D3211yescharacteristic
352Q16—184no—
353SD16—184no—
354M16—61no—
355M16—61no—
356M16—92no—
357M16—181no—
358M16—181no—
359M16—181no—
360C2×C8—32no—
361C2×C8—61no—
362C2×C8—61no—
363C2×C8—61no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3—121no—
380C22×C3#88311yescharacteristic
381C22×C3#88511yescharacteristic
382C22×C3#88511yescharacteristic
383C22×C3#88611yescharacteristic
384C22×C3#93811yescharacteristic
385C22×C3#93911yescharacteristic
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—82no—
394C3×C4—81no—
395C3×C4—81no—
396C3×C4—122no—
397C3×C4—121no—
398C3×C4#88211yescharacteristic
399C3×C4#88311yescharacteristic
400C3×C4#88411yescharacteristic
401C3×C4#88411yescharacteristic
402C3×C4#92911yescharacteristic
403C3×C4#93011yescharacteristic
404C3×C4#93711yescharacteristic
405C3×C4#93911yescharacteristic
406Dic3—41no—
407Dic3—42no—
408C32#205211yescharacteristic, complemented, Sylow
409C23—61no—
410C23#380511yescharacteristic
411Q8—61no—
412Q8—62no—
413Q8—62no—
414Q8—61no—
415Q8—121no—
416Q8—121no—
417D4—61no—
418D4—61no—
419D4—121no—
420D4—121no—
421C2×C4—41no—
422C2×C4—62no—
423C2×C4—61no—
424C2×C4—81no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4#379511yescharacteristic
430C2×C4#379811yescharacteristic
431C2×C4D3×D1211yescharacteristic
432C2×C4#380211yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C2×C4D3×#6711yescharacteristic
435C8—62no—
436C8—121no—
437C8—182no—
438C8—361no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—241no—
449C2×C3#495911yescharacteristic
450C2×C3#496111yescharacteristic
451C2×C3#517711yescharacteristic
452C2×C3#519211yescharacteristic
453C2×C3#520011yescharacteristic
454C2×C3#520411yescharacteristic
455D3—81no—
456C22—21no—
457C22—21no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22#6389111yescharacteristic
462C22#6391511yescharacteristic
463C22#6397011yescharacteristic
464C4—81no—
465C4—121no—
466C4—122no—
467C4#6388511yescharacteristic
468C4#6390511yescharacteristic
469C4#6390611yescharacteristic
470C4#6392211yescharacteristic
471C3—21no—
472C3#7026411yescharacteristic, complemented
473C3#7031011yescharacteristic, complemented
474C2—21no—
475C2—21no—
476C2—241no—
477C2#1059139011yescharacteristic
478C2#1059150611yescharacteristic
479C2#1059164111yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×C3×#235C22
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
2. C2×C3×#810C2semidirect
4. C2×#63577C2semidirect
5. C2×#63560C2semidirect
7. #10589396C2semidirect
37. C2×#810D3semidirect
408. C32#2052semidirect
472. C3#70264semidirect
473. C3#70310semidirect

Maximal subgroups

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

subgroupindex
C2×#638272
C2×C3×#8102
C3×#49662
C2×#635772
C2×#635602
#105910702
#105893962
#703103
#702643