Finite Group Databasebeta

← #11787032

Subgroups — #11787032

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2#10592818C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic
4C2×C3×#822C211yesmaximal, characteristic, complemented
5#10591084C211yesmaximal, characteristic
6#10589162C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70722—31nomaximal
9#70376—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815—22no—
20C2×D3×C3⋊C8—21no—
21#63641—21no—
22#63641—21no—
23C3×#825—22no—
24C3×#822—22no—
25#63566C411yescharacteristic, complemented
26#63566C411yescharacteristic, complemented
27#63563C411yescharacteristic, complemented
28#63563C411yescharacteristic, complemented
29C2×#948—31no—
30C2×#907—31no—
31C2×C3×#108—31no—
32C2×C3×#104—31no—
33#5233—31no—
34C2×#825D311yescharacteristic
35C2×#822D311yescharacteristic, complemented
36#5119—31no—
37#5119—31no—
38#5119—61no—
39#5113—31no—
40#4555—31no—
41#4550—31no—
42#4524—31no—
43#4523—31no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235D412yes—
50C3×#235Q812yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×M16—21no—
55C32×M16—21no—
56C2×C32×C8—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60C4×C3⋊Dic3—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D411yescharacteristic
64C2×C3⋊(C3⋊C8)D411yescharacteristic
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⋊C8C2×C411yescharacteristic
73C2×C3×C3⋊C8C2×C411yescharacteristic
74#3711—24no—
75D3×C3⋊C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—21no—
80C2×C3×M16—31no—
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C2×D311yescharacteristic
83C22×C3×C8—31no—
84C2×C3×C42—31no—
85#948—62no—
86#948—62no—
87#926—31no—
88#926—31no—
89#926—61no—
90C2×C4×Dic3C2×D311yescharacteristic
91C2×#208—61no—
92C2×#208C2×D311yescharacteristic
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—61no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98#907—62no—
99#907—62no—
100C2×ΓL(1,𝔽25)—61no—
101C2×D3×C8—61no—
102C3×#108—62no—
103C3×#104—62no—
104#835—31no—
105#835—31no—
106#832—31no—
107#832—31no—
108#825—22no—
109#822—22no—
110#821—31no—
111#821—31no—
112#816—31no—
113#816—31no—
114Dic3⋊C8—61no—
115Dic3⋊C8—61no—
116Dic3⋊C8—61no—
117Dic3⋊C8—61no—
118Dic3⋊C8—62no—
119Dic3⋊C8—62no—
120C23×C32#4111yescharacteristic
121C22×C3×D3—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C3×#67—22no—
131C3×#67—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yes—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yes—
142C32×C8—41no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—21no—
145C3×C3⋊C8—21no—
146C3×C3⋊C8—21no—
147C3×C3⋊C8—22no—
148C2×#131—91no—
149C2×#108—31no—
150#424—91no—
151C2×#104—31no—
152#416—91no—
153#339—91no—
154#336—91no—
155C3×#41—32no—
156C3×#41—32no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
168C22×Dic3—21no—
169#235—21no—
170#235—21no—
171#235Dic612yes—
172#235#6712yes—
173C2×D12C4×D311yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6C4×D311yescharacteristic
176C3×M16—21no—
177C3×M16—21no—
178C3×M16—21no—
179C3×M16—21no—
180C3×M16—32no—
181C3×M16—41no—
182C3×M16—41no—
183C3×M16—61no—
184C2×C3×C8—22no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—31no—
188C2×C3×C8—31no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C42—61no—
193C3×C42—61no—
194#217—62no—
195#217—61no—
196#217—61no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—31no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3—62no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208#208—21no—
209#208—64no—
210#208#6712yes—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—31no—
215C2×C3⋊C8—31no—
216C2×C3⋊C8—31no—
217C2×C3⋊C8—31no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—64no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—121no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8C4×D311yescharacteristic
228C2×C3⋊C8C4×D311yescharacteristic
229ΓL(1,𝔽25)—64no—
230D3×C8—64no—
231C22×C32—21no—
232C22×C32—21no—
233C22×C32C4×D411yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C22×C32#12311yescharacteristic
236C2×C3×D3—22no—
237C2×C3×D3—41no—
238C2×C3×D3—41no—
239C32×C4C2×C4⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12011yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C3⋊Dic3—41no—
244C3⋊Dic3—41no—
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248#131—182no—
249#131—182no—
250C2×M16—31no—
251C2×M16—181no—
252C2×M16D3211yescharacteristic
253C22×C8—31no—
254C22×C8—91no—
255C22×C8—181no—
256#117—91no—
257C2×C42—31no—
258#108—62no—
259C4⋊C8—181no—
260C4⋊C8—181no—
261#104—62no—
262#103—91no—
263#103—91no—
264#102—91no—
265#102—91no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3#23711yescharacteristic
269C23×C3#23911yescharacteristic
270C22×D3—21no—
271C3×Q8—32no—
272C3×Q8—61no—
273C3×D4—32no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4C2×Dic611yescharacteristic
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4D3×Q811yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301#67—22no—
302#67—22no—
303C2×Dic3—21no—
304C2×Dic3—22no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313D12—21no—
314D12Dic3⋊C412yes—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6Dic3⋊C412yes—
319C3×C8—42no—
320C3×C8—41no—
321C3×C8—41no—
322C3×C8—61no—
323C3×C8—61no—
324C3×C8—62no—
325C3⋊C8—21no—
326C3⋊C8—21no—
327C3⋊C8—22no—
328C3⋊C8—61no—
329C3⋊C8—61no—
330C3⋊C8—61no—
331C3⋊C8—61no—
332C3⋊C8—121no—
333C3⋊C8—121no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38511yescharacteristic
337C2×C32#44311yescharacteristic
338C2×C32#44411yescharacteristic
339C3×D3—42no—
340#41—32no—
341#41—32no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4C2×D3211yescharacteristic
350M16—21no—
351M16—21no—
352M16—32no—
353M16—61no—
354M16—184no—
355C2×C8—21no—
356C2×C8—31no—
357C2×C8—31no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8—184no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4—91no—
367C4⋊C4—91no—
368C22⋊C4—181no—
369C42—61no—
370C42—61no—
371C42—181no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3#87811yescharacteristic
385C22×C3#67⋊C411yescharacteristic
386C22×C3#89311yescharacteristic
387C22×C3#89411yescharacteristic
388C22×C3#93511yescharacteristic
389C22×C3#94611yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—62no—
398C3×C4—122no—
399C3×C4#87811yescharacteristic
400C3×C4#67⋊C411yescharacteristic
401C3×C4D3×C4⋊C411yescharacteristic
402C3×C4#89611yescharacteristic
403C3×C4C2×Dic3⋊C411yescharacteristic
404C3×C4C4×#6711yescharacteristic
405C3×C4#93711yescharacteristic
406C3×C4#93711yescharacteristic
407Dic3—22no—
408Dic3—42no—
409Dic3—122no—
410Dic3—122no—
411Dic3—121no—
412Dic3—121no—
413Dic3—121no—
414Dic3—121no—
415C32#186611yescharacteristic, complemented, Sylow
416C23—61no—
417C23#379611yescharacteristic
418Q8—32no—
419Q8—61no—
420D4—32no—
421D4—62no—
422D4—62no—
423D4—61no—
424C2×C4—61no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4D3×Dic611yescharacteristic
433C2×C4#379511yescharacteristic
434C2×C4C4×D3211yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C2×C4#381111yescharacteristic
438C8—41no—
439C8—61no—
440C8—61no—
441C8—62no—
442C8—181no—
443C8—181no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—122no—
454C2×C3#482311yescharacteristic
455C2×C3#482411yescharacteristic
456C2×C3#489411yescharacteristic
457C2×C3#489511yescharacteristic
458C2×C3#494611yescharacteristic
459C2×C3#498911yescharacteristic
460D3—42no—
461C22—21no—
462C22—21no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22#6388111yescharacteristic
467C22#6388411yescharacteristic
468C22#6388711yescharacteristic
469C4—62no—
470C4—122no—
471C4—361no—
472C4—361no—
473C4D3×Dic3⋊C411yescharacteristic
474C4#6387911yescharacteristic
475C4#6389611yescharacteristic
476C4#6398311yescharacteristic
477C3—21no—
478C3#7037611yescharacteristic, complemented
479C3#7072211yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—122no—
483C2#1059097711yescharacteristic
484C2#1059097811yescharacteristic
485C2#1059137211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592818C2semidirect
4. C2×C3×#822C2semidirect
6. #10589162C2semidirect
7. #10589155C2semidirect
25. #63566C4semidirect
26. #63566C4semidirect
27. #63563C4semidirect
28. #63563C4semidirect
35. C2×#822D3semidirect
415. C32#1866semidirect
478. C3#70376semidirect
479. C3#70722semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
#105928182
C2×C3×#8252
C2×C3×#8222
#105910842
#105891622
#105891552
#707223
#703763