Finite Group Databasebeta

← #11785594

Subgroups — #11785594

Order 1152.

609 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2#10592665C211yesmaximal, characteristic
3C2×C3×#808C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70592—31nomaximal
9#69000—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—21no—
18#63817—22no—
19#63817C414yescomplemented
20C2×#3710—21no—
21#63637—21no—
22#63636—21no—
23C3×#808—21no—
24C3×#808—21no—
25#63577—22no—
26#63567—21no—
27#63564—21no—
28C2×#907—31no—
29C2×#901—31no—
30C2×C3×#106—31no—
31#5133—31no—
32C2×#822—31no—
33C2×#819—31no—
34#4966—31no—
35#4966—31no—
36#4966—31no—
37#4966—61no—
38C2×#808D311yescharacteristic, complemented
39C3×#343—31no—
40#4554—31no—
41#4530—31no—
42#4530D311yescharacteristic, complemented
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828Q812yes—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56#3748—21no—
57#3748—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×#208—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208C2×C412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D412yes—
69C2×C3×C3⋊C8D411yescharacteristic
70C2×C3×C3⋊C8D411yescharacteristic
71#3712—24no—
72#3710—24no—
73#1815—91noSylow
74C2×#235—31no—
75C2×#235—31no—
76C2×#235—61no—
77C2×C3×M16—31no—
78C2×C3×M16—31no—
79C22×C3×C8—31no—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4C2×D311yescharacteristic
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×#208—31no—
86C2×#208—31no—
87C2×#208—61no—
88C2×#208C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
90C22×C3⋊C8C2×D311yescharacteristic
91#907—34no—
92#907—62no—
93#901—34no—
94#901—62no—
95C2×ΓL(1,𝔽25)—61no—
96C2×ΓL(1,𝔽25)—61no—
97C2×D3×C8—61no—
98C2×D3×C8—61no—
99C3×#106—61no—
100C3×#106—61no—
101#822—62no—
102#821—61no—
103#819—62no—
104#816—61no—
105#810—61no—
106#810—61no—
107#810—61no—
108#810—62no—
109#809—61no—
110#809—61no—
111#809—61no—
112#809—62no—
113#808—21no—
114#808—21no—
115C23×C32#4111yescharacteristic
116C22×C3⋊D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4—81no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—22no—
126#638—22no—
127C2×C3⋊Dic3—21no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)C4⋊C412yes—
130C4×C3⋊D3—22no—
131C4×C3⋊D3—22no—
132#634—21no—
133#634C4⋊C412yes—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—81no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8C22⋊C412yes—
140C3×C3⋊C8C22⋊C412yes—
141C2×#131—91no—
142C2×#108—91no—
143C2×#106—31no—
144#417—91no—
145#417—91no—
146#343—31no—
147#343—91no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—41no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C2×#67—61no—
156C2×#67—61no—
157C2×#67—121no—
158C22×Dic3—21no—
159#235—32no—
160#235—32no—
161#235—32no—
162#235—32no—
163#235—62no—
164#235—62no—
165#235—61no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—121no—
170#235—121no—
171C2×D12—31no—
172C2×D12—31no—
173C2×D12—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—121no—
177C2×Dic6—31no—
178C2×Dic6—31no—
179C2×Dic6—61no—
180C3×M16—32no—
181C3×M16—61no—
182C3×M16—61no—
183C3×M16—61no—
184C2×C3×C8—32no—
185C2×C3×C8—32no—
186C2×C3×C8—31no—
187C2×C3×C8—31no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200#208—21no—
201#208—21no—
202#208—21no—
203#208—61no—
204#208—61no—
205#208—61no—
206#208—61no—
207#208—121no—
208#208—121no—
209#208C4×D312yes—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—62no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8C4×D312yes—
216C2×C3⋊C8D1212yes—
217C2×C3⋊C8#6711yescharacteristic
218C2×C3⋊C8#6711yescharacteristic
219ΓL(1,𝔽25)—64no—
220ΓL(1,𝔽25)—64no—
221D3×C8—64no—
222D3×C8—64no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32#11711yescharacteristic
226C22×C32#12111yescharacteristic
227C22×C32C22⋊Q811yescharacteristic
228C2×C3⋊D3—22no—
229C2×C3⋊D3—41no—
230C2×C3⋊D3—41no—
231C32×C4—81no—
232C32×C4C2×C22⋊C411yescharacteristic
233C32×C4C2×C4⋊C411yescharacteristic
234C32×C4#12111yescharacteristic
235C32×C4C22⋊Q811yescharacteristic
236C3⋊Dic3—22no—
237C3×Dic3—81no—
238C2×#41—91no—
239#131—94no—
240#131—182no—
241C2×M16—31no—
242C2×M16—31no—
243C2×M16—91no—
244C2×M16—181no—
245C22×C8—31no—
246C22×C8—181no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4D3211yescharacteristic
249#108—182no—
250#106—61no—
251#106—61no—
252#103—181no—
253#103—181no—
254#102—181no—
255#102—181no—
256C23×C3—21no—
257C23×C3#23511yescharacteristic
258C23×C3#23711yescharacteristic
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—121no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—42no—
269C2×C3×C4—41no—
270C2×C3×C4—41no—
271C2×C3×C4—82no—
272C2×C3×C4—81no—
273C2×C3×C4—81no—
274C2×C3×C4—121no—
275C2×C3×C4—241no—
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4#23511yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×Q811yescharacteristic
285C2×C3×C4D3×Q811yescharacteristic
286C2×C3×C4#23911yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288#67—62no—
289#67—62no—
290#67—62no—
291#67—62no—
292#67—122no—
293#67—122no—
294C2×Dic3—41no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—81no—
298C2×Dic3—121no—
299D12—32no—
300D12—32no—
301D12—62no—
302D12—61no—
303D12—61no—
304D12—121no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—62no—
308C4×D3—62no—
309C4×D3—122no—
310C4×D3—122no—
311Dic6—32no—
312Dic6—32no—
313Dic6—62no—
314Dic6—61no—
315Dic6—61no—
316Dic6—121no—
317C3×C8—32no—
318C3×C8—32no—
319C3×C8—62no—
320C3×C8—121no—
321C3⋊C8—22no—
322C3⋊C8—41no—
323C3⋊C8—122no—
324C3⋊C8—121no—
325C3⋊C8—121no—
326C3⋊C8(C2×D3)⋊C412yes—
327C3⋊C8(C2×D3)⋊C412yes—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32#38011yescharacteristic
331C2×C32#47111yescharacteristic
332C2×C32#47111yescharacteristic
333C3⋊D3—42no—
334#41—92no—
335#41—92no—
336#41—181no—
337#41—181no—
338C2×Q8—91no—
339C2×D4—91no—
340C2×D4—181no—
341C22×C4—21no—
342C22×C4—61no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345M16—32no—
346M16—61no—
347M16—61no—
348M16—61no—
349M16—184no—
350M16—181no—
351M16—181no—
352C2×C8—32no—
353C2×C8—32no—
354C2×C8—31no—
355C2×C8—31no—
356C2×C8—61no—
357C2×C8—61no—
358C2×C8—184no—
359C2×C8—181no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3#87211yescharacteristic
374C22×C3#88411yescharacteristic
375C22×C3#89211yescharacteristic
376C22×C3#89611yescharacteristic
377C22×C3#89711yescharacteristic
378C22×C3#93811yescharacteristic
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—122no—
382C2×D3—121no—
383C2×D3—121no—
384C2×D3—121no—
385C2×D3—121no—
386C2×D3—241no—
387C2×D3—241no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—82no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—241no—
396C3×C4D3×C22⋊C411yescharacteristic
397C3×C4#88411yescharacteristic
398C3×C4D3×C4⋊C411yescharacteristic
399C3×C4D3×C4⋊C411yescharacteristic
400C3×C4#89511yescharacteristic
401C3×C4#89611yescharacteristic
402C3×C4C2×(C2×D3)⋊C411yescharacteristic
403C3×C4#94611yescharacteristic
404Dic3—62no—
405Dic3—62no—
406Dic3—81no—
407Dic3—122no—
408C32#181511yescharacteristic, complemented, Sylow
409C23—181no—
410C23#380411yescharacteristic
411Q8—92no—
412Q8—181no—
413D4—92no—
414D4—182no—
415D4—182no—
416D4—181no—
417C2×C4—41no—
418C2×C4—81no—
419C2×C4—121no—
420C2×C4—181no—
421C2×C4—182no—
422C2×C4—182no—
423C2×C4—241no—
424C2×C4#379711yescharacteristic
425C2×C4#379911yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4D3×D1211yescharacteristic
428C2×C4D3×#6711yescharacteristic
429C2×C4#381111yescharacteristic
430C8—32no—
431C8—32no—
432C8—62no—
433C8—121no—
434C8—361no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3#466711yescharacteristic
445C2×C3#474811yescharacteristic
446C2×C3#475411yescharacteristic
447C2×C3#498711yescharacteristic
448C2×C3#517711yescharacteristic
449C2×C3#517711yescharacteristic
450D3—122no—
451D3—122no—
452D3—242no—
453C22—21no—
454C22—21no—
455C22—182no—
456C22—361no—
457C22—361no—
458C22#6383611yescharacteristic
459C22#6389511yescharacteristic
460C22#6395811yescharacteristic
461C4—81no—
462C4—182no—
463C4—241no—
464C4#6388311yescharacteristic
465C4#6388811yescharacteristic
466C4#6391011yescharacteristic
467C4D3×(C2×D3)⋊C411yescharacteristic
468C3—21no—
469C3#6900011yescharacteristic, complemented
470C3#7059211yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—362no—
474C2#1059136711yescharacteristic
475C2#1059140711yescharacteristic
476C2#1059154211yescharacteristic
subgroupG/H
centerC22#63958
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1815
LCSG ▷ C2×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×#808C2semidirect
4. C2×#63577C2semidirect
6. C3×#4530C2semidirect
7. #10589167C2semidirect
19. #63817C4semidirect
38. C2×#808D3semidirect
42. #4530D3semidirect
408. C32#1815semidirect
469. C3#69000semidirect
470. C3#70592semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105926652
C2×C3×#8082
C2×#635772
#105911062
C3×#45302
#105891672
#705923
#690003