Finite Group Databasebeta

← #11785595

Subgroups — #11785595

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C3×#4966C211yesmaximal, characteristic
3C2×C3×#808C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic
6#10589396C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70592—31nomaximal
9#70299—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63814—22no—
19#63814C414yescomplemented
20C2×D3×C3⋊C8—21no—
21C3×#810—21no—
22C3×#809—21no—
23C3×#808—21no—
24C3×#808—21no—
25#63577—22no—
26#63565—21no—
27#63562—21no—
28C2×#948—31no—
29C2×#901—31no—
30C2×C3×#106—31no—
31C3×#417—31no—
32#5232—31no—
33C2×#822—31no—
34C2×#819—31no—
35#4966—31no—
36#4966D311yescharacteristic
37C2×#808D311yescharacteristic, complemented
38#4554—31no—
39#4530—31no—
40#4530—31no—
41#4530—31no—
42#4530—61no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235Q812yes—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56#3748—21no—
57#3748—21no—
58#3748—21no—
59#3748C2×C412yes—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×#208—21no—
65C3×#208—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8D412yes—
69C2×C3×C3⋊C8D411yescharacteristic
70C2×C3×C3⋊C8D411yescharacteristic
71#3711—24no—
72D3×C3⋊C8—24no—
73#1815—91noSylow
74C2×C3×#41—31no—
75C2×#235C2×D311yescharacteristic
76C2×C3×M16—31no—
77C22×C3×C8—31no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82#948—34no—
83#948—62no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×#208—31no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—31no—
89C2×#208—61no—
90C2×#208—61no—
91C2×#208—61no—
92C2×#208C2×D311yescharacteristic
93C22×C3⋊C8—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95#901—34no—
96#901—62no—
97C2×ΓL(1,𝔽25)—61no—
98C2×D3×C8—61no—
99C3×#106—61no—
100C3×#106—61no—
101C3×#103—61no—
102C3×#102—61no—
103#835—61no—
104#832—61no—
105#822—62no—
106#819—62no—
107#810—21no—
108#810—61no—
109#809—21no—
110#809—61no—
111#808—21no—
112#808—21no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4—81no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C3×#67—22no—
124C3×#67—22no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C3×D12—21no—
129C3×D12C4⋊C412yes—
130C3×C4×D3—22no—
131C3×C4×D3—22no—
132C3×Dic6—21no—
133C3×Dic6C4⋊C412yes—
134C3⋊(C3⋊C8)—22no—
135C3⋊(C3⋊C8)—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8C22⋊C412yes—
138C3×C3⋊C8C22⋊C412yes—
139C2×#131—91no—
140C2×#108—91no—
141C2×#106—31no—
142#417—31no—
143#417—91no—
144#343—91no—
145#343—91no—
146C3×#41—32no—
147C3×#41—32no—
148C3×#41—61no—
149C3×#41—61no—
150C2×C3×Q8—31no—
151C2×C3×D4—31no—
152C2×C3×D4—61no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163#235—21no—
164#235—21no—
165#235Dic612yes—
166#235C4×D312yes—
167C2×D12#6711yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6#6711yescharacteristic
170C3×M16—61no—
171C3×M16—61no—
172C2×C3×C8—32no—
173C2×C3×C8—32no—
174C2×C3×C8—31no—
175C2×C3×C8—31no—
176C2×C3×C8—61no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—41no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187#208—21no—
188#208—21no—
189#208—32no—
190#208—32no—
191#208—62no—
192#208—61no—
193#208—61no—
194#208—64no—
195#208—62no—
196#208—61no—
197#208—61no—
198#208—61no—
199#208—61no—
200#208—121no—
201#208—121no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—64no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8C4×D312yes—
211C2×C3⋊C8D1212yes—
212C2×C3⋊C8#6711yescharacteristic
213C2×C3⋊C8#6711yescharacteristic
214ΓL(1,𝔽25)—64no—
215D3×C8—64no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32#11711yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C2×C3×D3—22no—
222C2×C3×D3—41no—
223C2×C3×D3—41no—
224C32×C4—81no—
225C32×C4C2×C22⋊C411yescharacteristic
226C32×C4C2×C4⋊C411yescharacteristic
227C32×C4#12111yescharacteristic
228C32×C4C22⋊Q811yescharacteristic
229C3×Dic3—22no—
230C3×Dic3—81no—
231C2×#41—31no—
232#131—94no—
233#131—182no—
234C2×M16—31no—
235C2×M16—91no—
236C2×M16—91no—
237C2×M16—181no—
238C22×C8—31no—
239C22×C8—181no—
240C2×C4⋊C4—31no—
241C2×C4⋊C4D3211yescharacteristic
242#108—182no—
243#106—61no—
244#106—61no—
245#103—61no—
246#103—181no—
247#102—61no—
248#102—181no—
249C23×C3—21no—
250C23×C3—61no—
251C23×C3#23711yescharacteristic
252C23×C3#23711yescharacteristic
253C22×D3—21no—
254C3×Q8—32no—
255C3×Q8—61no—
256C3×D4—32no—
257C3×D4—62no—
258C3×D4—62no—
259C3×D4—61no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—42no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—61no—
270C2×C3×C4—62no—
271C2×C3×C4—62no—
272C2×C3×C4—81no—
273C2×C3×C4—81no—
274C2×C3×C4—82no—
275C2×C3×C4—121no—
276C2×C3×C4—241no—
277C2×C3×C4C2×Dic611yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4D3×Q811yescharacteristic
286C2×C3×C4#23911yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289#67—22no—
290#67—22no—
291C2×Dic3—21no—
292C2×Dic3—41no—
293C2×Dic3—81no—
294D12—21no—
295D12Dic3⋊C412yes—
296C4×D3—22no—
297C4×D3—22no—
298Dic6—21no—
299Dic6Dic3⋊C412yes—
300C3×C8—32no—
301C3×C8—32no—
302C3×C8—121no—
303C3⋊C8—41no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C3⋊C8—122no—
307C3⋊C8—122no—
308C3⋊C8—121no—
309C3⋊C8—121no—
310C3⋊C8(C2×D3)⋊C412yes—
311C3⋊C8(C2×D3)⋊C412yes—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#38011yescharacteristic
315C2×C32#47111yescharacteristic
316C2×C32#47111yescharacteristic
317C3×D3—42no—
318#41—32no—
319#41—32no—
320#41—61no—
321#41—61no—
322C2×Q8—31no—
323C2×D4—31no—
324C2×D4—61no—
325C22×C4—21no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4C2×D3211yescharacteristic
329M16—61no—
330M16—61no—
331M16—92no—
332M16—184no—
333M16—181no—
334M16—181no—
335M16—181no—
336C2×C8—32no—
337C2×C8—32no—
338C2×C8—31no—
339C2×C8—31no—
340C2×C8—61no—
341C2×C8—184no—
342C2×C8—181no—
343C2×C8—181no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—62no—
358C22×C3—121no—
359C22×C3—121no—
360C22×C3#87711yescharacteristic
361C22×C3#87811yescharacteristic
362C22×C3#89211yescharacteristic
363C22×C3#89711yescharacteristic
364C22×C3#93811yescharacteristic
365C22×C3#93911yescharacteristic
366C2×D3—22no—
367C2×D3—41no—
368C2×D3—41no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—62no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—241no—
378C3×C4#87811yescharacteristic
379C3×C4D3×C22⋊C411yescharacteristic
380C3×C4D3×C4⋊C411yescharacteristic
381C3×C4#89511yescharacteristic
382C3×C4C2×Dic3⋊C411yescharacteristic
383C3×C4C2×(C2×D3)⋊C411yescharacteristic
384C3×C4#93911yescharacteristic
385C3×C4#94611yescharacteristic
386Dic3—22no—
387Dic3—81no—
388C32#181511yescharacteristic, complemented, Sylow
389C23—61no—
390C23#380511yescharacteristic
391Q8—32no—
392Q8—61no—
393D4—32no—
394D4—62no—
395D4—62no—
396D4—61no—
397C2×C4—41no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—81no—
402C2×C4—121no—
403C2×C4—241no—
404C2×C4D3×Dic611yescharacteristic
405C2×C4#379611yescharacteristic
406C2×C4C4×D3211yescharacteristic
407C2×C4D3×D1211yescharacteristic
408C2×C4D3×#6711yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C8—32no—
411C8—32no—
412C8—121no—
413C8—182no—
414C8—361no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—122no—
425C2×C3#494211yescharacteristic
426C2×C3#498711yescharacteristic
427C2×C3#517711yescharacteristic
428C2×C3#517711yescharacteristic
429C2×C3#520011yescharacteristic
430C2×C3#520311yescharacteristic
431D3—42no—
432C22—21no—
433C22—21no—
434C22—62no—
435C22—121no—
436C22—121no—
437C22#6387811yescharacteristic
438C22#6389311yescharacteristic
439C22#6397011yescharacteristic
440C4—62no—
441C4—81no—
442C4—241no—
443C4D3×Dic3⋊C411yescharacteristic
444C4#6388611yescharacteristic
445C4#6388711yescharacteristic
446C4D3×(C2×D3)⋊C411yescharacteristic
447C3—21no—
448C3#7029911yescharacteristic, complemented
449C3#7059211yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—122no—
453C2#1059136611yescharacteristic
454C2#1059150611yescharacteristic
455C2#1059164211yescharacteristic
subgroupG/H
centerC22#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×C3×#235C22
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. #10589396C2semidirect
7. #10589167C2semidirect
19. #63814C4semidirect
37. C2×#808D3semidirect
388. C32#1815semidirect
448. C3#70299semidirect
449. C3#70592semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C3×#49662
C2×C3×#8082
C2×#635772
#105910872
#105893962
#105891672
#705923
#702993