Finite Group Databasebeta

← #10698699

Subgroups — #10698699

Order 768.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#74368C211yesmaximal, characteristic
2#70479C211yesmaximal, characteristic, complemented
3#70479C211yesmaximal, characteristic, complemented
4C2×#4483C211yesmaximal, characteristic, complemented
5C2×#4483C211yesmaximal, characteristic, complemented
6#69574C211yesmaximal, characteristic, complemented
7C3×#1296C211yesmaximal, characteristic, complemented
8#10431—31nomaximal, Sylow
9C2×#895—21no—
10C2×#895—21no—
11C2×C4×D12C2211yescharacteristic
12C2×C4×D12C2211yescharacteristic
13C2×C3×C4⋊C8C2211yescharacteristic
14C2×C3×C4⋊C8C2211yescharacteristic
15C3×#384C2211yescharacteristic
16C2×#821—21no—
17C2×#821—21no—
18#4991—22no—
19#4987—21no—
20#4987—21no—
21#4935C2211yescharacteristic
22C2×C4×C3⋊C8C2211yescharacteristic
23#4551—21no—
24#4551—21no—
25#4529—22no—
26#4483—22no—
27#4483—22no—
28#2537—31no—
29#1834—31no—
30#1802—31no—
31#1802—31no—
32C2×D4⋊C8—31no—
33C2×D4⋊C8—31no—
34#1296D311yescharacteristic, complemented
35C22×D12—22no—
36C22×D12D411yescharacteristic
37C22×D12D411yescharacteristic
38C22×C4×D3—21no—
39C22×C4×D3—21no—
40C22×C3×C8—21no—
41C22×C3×C8—21no—
42C2×C3×C4⋊C4—21no—
43C2×C3×C4⋊C4—21no—
44C2×C3×C4⋊C4D412yes—
45C2×C3×C42C2311yescharacteristic
46C2×(C2×D3)⋊C4—22no—
47C2×(C2×D3)⋊C4—22no—
48C2×(C2×D3)⋊C4—21no—
49C2×(C2×D3)⋊C4—21no—
50C2×C4⋊Dic3—21no—
51C2×C4⋊Dic3—21no—
52C2×C4⋊Dic3—21no—
53C2×C4⋊Dic3D411yescharacteristic
54C2×C4⋊Dic3D411yescharacteristic
55C22×C3⋊C8—21no—
56#895—42no—
57#895—42no—
58#895—42no—
59#895—42no—
60C4×D12—21no—
61C4×D12—21no—
62C4×D12—21no—
63C4×D12—21no—
64C4×D12—21no—
65C4×D12—21no—
66C4×D12—21no—
67C4×D12—21no—
68C3×C4⋊C8—21no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8—21no—
72C3⋊#95—22no—
73#821—42no—
74#821—42no—
75C4×C3⋊C8—21no—
76C4×C3⋊C8D412yescomplemented
77C2×#121—61no—
78C2×#121—61no—
79C2×C4×D4—31no—
80C2×C4×D4—31no—
81C2×C4⋊C8C2×D311yescharacteristic
82C2×C4⋊C8C2×D311yescharacteristic
83C2×#102—61no—
84C2×#102—61no—
85C2×C4×C8—31no—
86#394—62no—
87#384—31no—
88#384C2×D311yescharacteristic
89#380—61no—
90#380—61no—
91#340—61no—
92#340—61no—
93#340—62no—
94D4⋊C8—62no—
95D4⋊C8—62no—
96C23×D3—21no—
97C23×D3—21no—
98C22×C3×C4—22no—
99C22×C3×C4C2×D411yescharacteristic
100C22×C3×C4C2×D411yescharacteristic
101C22×C3×C4C2×D411yescharacteristic
102C22×Dic3—21no—
103C22×Dic3—21no—
104C22×Dic3—41no—
105C2×D12—21no—
106C2×D12—21no—
107C2×D12—21no—
108C2×D12—21no—
109C2×D12—21no—
110C2×D12—21no—
111C2×D12—21no—
112C2×D12—21no—
113C2×D12—21no—
114C2×D12—21no—
115C2×D12—44no—
116C2×D12—44no—
117C2×D12—82no—
118C2×D12D812yes—
119C2×D12SD1612yes—
120C2×C4×D3—41no—
121C2×C4×D3—41no—
122C2×C4×D3—41no—
123C2×C4×D3—41no—
124C2×C4×D3—41no—
125C2×C4×D3—41no—
126C2×C4×D3—41no—
127C2×C4×D3—41no—
128C2×C4×D3—41no—
129C2×C4×D3—41no—
130C2×C4×D3—41no—
131C2×C4×D3—41no—
132C2×C3×C8—41no—
133C2×C3×C8—41no—
134C2×C3×C8—41no—
135C2×C3×C8—41no—
136C2×C3×C8—41no—
137C2×C3×C8—41no—
138C3×C4⋊C4—42no—
139C3×C4⋊C4—41no—
140C3×C4⋊C4—41no—
141C3×C4⋊C4—41no—
142C3×C4⋊C4—41no—
143C3×C42C2×D411yescharacteristic
144C3×C42#4111yescharacteristic
145C3×C42#4111yescharacteristic
146C3×C42#4111yescharacteristic
147(C2×D3)⋊C4—44no—
148(C2×D3)⋊C4—44no—
149(C2×D3)⋊C4—41no—
150(C2×D3)⋊C4—41no—
151(C2×D3)⋊C4—41no—
152(C2×D3)⋊C4—41no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—42no—
158C4⋊Dic3—41no—
159C4⋊Dic3—41no—
160C4⋊Dic3—41no—
161C4⋊Dic3—41no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8—41no—
164C2×C3⋊C8—41no—
165C22×D4—31no—
166C22×D4—31no—
167C22×D4—62no—
168C23×C4—61no—
169C23×C4—61no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—61no—
173#121—122no—
174#121—122no—
175#121—122no—
176#121—122no—
177C4×D4—61no—
178C4×D4—61no—
179C4×D4—61no—
180C4×D4—61no—
181C4×D4—61no—
182C4×D4—61no—
183C4×D4—61no—
184C4×D4—61no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—31no—
188C2×C4⋊C4—31no—
189C2×C4⋊C4—61no—
190C2×C4⋊C4—61no—
191C2×C4⋊C4—61no—
192C2×C4⋊C4D1212yes—
193C2×C22⋊C4—62no—
194C2×C22⋊C4—62no—
195C2×C22⋊C4—61no—
196C2×C22⋊C4—61no—
197C2×C42C22×D311yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202#102—122no—
203#102—122no—
204C4×C8—32no—
205C4×C8—61no—
206#95—62no—
207C23×C3#12011yescharacteristic
208C22×D3—22no—
209C22×D3—22no—
210C22×D3—41no—
211C22×D3—41no—
212C22×D3—41no—
213C22×D3—41no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—41no—
217C22×D3—41no—
218C22×D3—41no—
219C22×D3—41no—
220C22×D3—41no—
221C22×D3—41no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4#12111yescharacteristic
228C2×C3×C4#12111yescharacteristic
229C2×C3×C4#12111yescharacteristic
230C2×C3×C4#12311yescharacteristic
231C2×C3×C4#12311yescharacteristic
232C2×C3×C4#12411yescharacteristic
233C2×C3×C4C2×D811yescharacteristic
234C2×C3×C4C2×SD1611yescharacteristic
235C2×C3×C4#13511yescharacteristic
236C2×C3×C4#13511yescharacteristic
237C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
238C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
239C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
240C2×C3×C4#13711yescharacteristic
241C2×Dic3—41no—
242C2×Dic3—41no—
243C2×Dic3—41no—
244C2×Dic3—41no—
245C2×Dic3—41no—
246C2×Dic3—41no—
247C2×Dic3—81no—
248C2×Dic3—81no—
249C2×Dic3—81no—
250D12—22no—
251D12—22no—
252D12—22no—
253D12—22no—
254D12—41no—
255D12—41no—
256D12—41no—
257D12—41no—
258D12—88no—
259C4×D3—81no—
260C4×D3—81no—
261C4×D3—81no—
262C4×D3—81no—
263C4×D3—81no—
264C4×D3—81no—
265C4×D3—81no—
266C4×D3—81no—
267C3×C8—81no—
268C3×C8—81no—
269C3⋊C8—42no—
270C24—61no—
271C24—61no—
272C2×D4—32no—
273C2×D4—32no—
274C2×D4—61no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283C2×D4—61no—
284C2×D4—124no—
285C2×D4—124no—
286C2×D4—242no—
287C22×C4—22no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4—121no—
291C22×C4—121no—
292C22×C4—121no—
293C22×C4—121no—
294C22×C4—121no—
295C22×C4—121no—
296C22×C4—121no—
297C22×C4—121no—
298C22×C4—121no—
299C22×C4—121no—
300C22×C4—121no—
301C22×C4—121no—
302C22×C4—121no—
303C22×C4C2×D1211yescharacteristic
304C22×C4D3×D411yescharacteristic
305C22×C4D3×D411yescharacteristic
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—62no—
313C2×C8—121no—
314C2×C8—121no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—122no—
325C4⋊C4—121no—
326C4⋊C4—121no—
327C4⋊C4—121no—
328C4⋊C4—121no—
329C22⋊C4—124no—
330C22⋊C4—124no—
331C22⋊C4—121no—
332C22⋊C4—121no—
333C22⋊C4—121no—
334C22⋊C4—121no—
335C42#23511yescharacteristic
336C42#23511yescharacteristic
337C42D3×D411yescharacteristic
338C42#23911yescharacteristic
339C22×C3#39411yescharacteristic
340C22×C3#44711yescharacteristic
341C22×C3#44911yescharacteristic
342C22×C3#45011yescharacteristic
343C22×C3#45211yescharacteristic
344C22×C3#45411yescharacteristic
345C22×C3#45511yescharacteristic
346C2×D3—42no—
347C2×D3—42no—
348C2×D3—42no—
349C2×D3—42no—
350C2×D3—42no—
351C2×D3—42no—
352C2×D3—81no—
353C2×D3—81no—
354C2×D3—81no—
355C2×D3—81no—
356C2×D3—81no—
357C2×D3—81no—
358C2×D3—81no—
359C2×D3—81no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—82no—
363C3×C4#46511yescharacteristic
364C3×C4#46611yescharacteristic
365C3×C4#46811yescharacteristic
366C3×C4#46911yescharacteristic
367C3×C4#48011yescharacteristic
368C3×C4#48111yescharacteristic
369C3×C4#48211yescharacteristic
370C3×C4#48211yescharacteristic
371Dic3—81no—
372Dic3—81no—
373Dic3—161no—
374C23—62no—
375C23—62no—
376C23—121no—
377C23—121no—
378C23—121no—
379C23—121no—
380C23—121no—
381C23—121no—
382C23—121no—
383C23—121no—
384C23—121no—
385C23—121no—
386C23—121no—
387C23—121no—
388C23#88211yescharacteristic
389D4—62no—
390D4—62no—
391D4—62no—
392D4—62no—
393D4—121no—
394D4—121no—
395D4—121no—
396D4—121no—
397D4—248no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—241no—
410C2×C4—241no—
411C2×C4—241no—
412C2×C4—241no—
413C2×C4—241no—
414C2×C4—241no—
415C2×C4—241no—
416C2×C4—241no—
417C2×C4—241no—
418C2×C4—241no—
419C2×C4—241no—
420C2×C4#87511yescharacteristic
421C2×C4#88411yescharacteristic
422C2×C4#88411yescharacteristic
423C2×C4#89411yescharacteristic
424C2×C4#89411yescharacteristic
425C2×C4#89511yescharacteristic
426C2×C4D3×D811yescharacteristic
427C2×C4#91111yescharacteristic
428C2×C4D3×SD1611yescharacteristic
429C2×C4#91411yescharacteristic
430C2×C4#91411yescharacteristic
431C2×C4#91611yescharacteristic
432C2×C4#91811yescharacteristic
433C2×C4#91911yescharacteristic
434C8—81no—
435C8—81no—
436C8—122no—
437C2×C3#162511yescharacteristic
438C2×C3#163511yescharacteristic
439C2×C3#163911yescharacteristic
440C2×C3#164611yescharacteristic
441C2×C3#203311yescharacteristic
442C2×C3#203411yescharacteristic
443C2×C3#204011yescharacteristic
444D3—82no—
445D3—82no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22—122no—
450C22—122no—
451C22—122no—
452C22—241no—
453C22—241no—
454C22—241no—
455C22—241no—
456C22—241no—
457C22—241no—
458C22—241no—
459C22—241no—
460C22#467211yescharacteristic
461C22#474611yescharacteristic
462C22#475311yescharacteristic
463C22#477311yescharacteristic
464C22#477611yescharacteristic
465C22#480811yescharacteristic
466C22#481011yescharacteristic
467C4—21no—
468C4—21no—
469C4—82no—
470C4—241no—
471C4—241no—
472C4—481no—
473C4#477511yescharacteristic
474C4#478211yescharacteristic
475C4#480711yescharacteristic
476C4#481211yescharacteristic
477C4#486311yescharacteristic
478C4#486611yescharacteristic
479C4#488211yescharacteristic
480C4#488511yescharacteristic
481C3#1043111yescharacteristic, complemented, Sylow
482C2—242no—
483C2—242no—
484C2#6839211yescharacteristic
485C2#6843211yescharacteristic
486C2#6843411yescharacteristic
487C2#6849511yescharacteristic
488C2#6882211yescharacteristic
489C2#6882311yescharacteristic
490C2#6897711yescharacteristic
subgroupG/H
centerC23#882
commutator, cosocleC2×C3×C42C23
FrattiniC2×C42C22×D3
FittingC3×#1296C2
socleC23×C3#120
prime radical#74368C2
hypercenter#1296D3
hypocenterC3#10431
LCSG ▷ C2×C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #70479C2semidirect
3. #70479C2semidirect
4. C2×#4483C2semidirect
5. C2×#4483C2semidirect
6. #69574C2semidirect
7. C3×#1296C2semidirect
34. #1296D3semidirect
76. C4×C3⋊C8D4semidirect
481. C3#10431semidirect

Maximal subgroups

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

subgroupindex
#743682
#704792
C2×#44832
#695742
C3×#12962
#104313