Finite Group Databasebeta

← #10690343

Subgroups — #10690343

Order 768.

594 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82745C211yesmaximal, characteristic
2C2×#5043C211yesmaximal, characteristic
3C2×C3×#328C211yesmaximal, characteristic
4#69924C211yesmaximal, characteristic
5#69423C211yesmaximal, characteristic
6#67674C211yesmaximal, characteristic
7#67612C211yesmaximal, characteristic
8#9044—31nomaximal, Sylow
9C2×C3×C22⋊Q8C2211yescharacteristic
10C22×C4⋊Dic3C2211yescharacteristic
11C2×C3×C22⋊C8C2211yescharacteristic
12C2×C3×#95C2211yescharacteristic
13#5229—21no—
14C2×#835—21no—
15#5212C2211yescharacteristic
16C2×C3⋊#95—21no—
17C2×C3⋊#95—21no—
18C2×C3⋊#95C2211yescharacteristic
19C2×#830C2211yescharacteristic
20#5043—22no—
21#5043C414yescomplemented
22#4984—21no—
23#4980—21no—
24#4980—21no—
25C2×#808—21no—
26#4950—21no—
27Dic3×C22⋊C4—21no—
28C3×#328—22no—
29#4551—21no—
30#4551—21no—
31C2×#483—31no—
32#2329—31no—
33#1823—31no—
34C2×#328D311yescharacteristic
35#1445—31no—
36#1294—31no—
37#1280—31no—
38C22×C3×Q8D411yescharacteristic
39C23×C3×C4—21no—
40C23×C3×C4C2311yescharacteristic
41C23×Dic3—21no—
42C23×Dic3D411yescharacteristic
43C23×Dic3D411yescharacteristic
44C22×C3×C8—21no—
45C3×C22⋊Q8—21no—
46C3×C22⋊Q8—21no—
47C3×C22⋊Q8C2×C412yes—
48C3×C22⋊Q8D412yes—
49C2×C3×C4⋊C4—21no—
50C2×C3×C4⋊C4D411yescharacteristic
51C2×C3×C22⋊C4—21no—
52C2×#217—21no—
53C2×C4⋊Dic3—21no—
54C2×C4⋊Dic3—21no—
55C2×C4⋊Dic3—21no—
56C2×C4⋊Dic3—21no—
57C2×C4⋊Dic3—21no—
58C2×C4⋊Dic3—21no—
59C2×C4⋊Dic3—21no—
60C2×C4⋊Dic3C2×C412yes—
61C2×C4⋊Dic3D411yescharacteristic
62C2×C4⋊Dic3D411yescharacteristic
63C2×C4×Dic3—21no—
64C2×C4×Dic3—21no—
65C22×C3⋊C8—21no—
66C3×C22⋊C8—21no—
67C3×C22⋊C8—21no—
68C3×#95—21no—
69C3×#95—21no—
70#835—24no—
71C3⋊#95—21no—
72C3⋊#95—21no—
73C3⋊#95—21no—
74C3⋊#95—21no—
75C3⋊#95—21no—
76C3⋊#95—21no—
77C3⋊#95—21no—
78C3⋊#95—42no—
79C3⋊#95—42no—
80#830—21no—
81#830C2×C412yes—
82#808—24no—
83C2×C22⋊Q8C2×D311yescharacteristic
84C22×C4⋊C4—31no—
85#483—34no—
86#483—62no—
87C2×#106—61no—
88C2×#103—61no—
89C2×C22⋊C8—31no—
90C2×C22⋊C8C2×D311yescharacteristic
91#391—61no—
92#389—61no—
93#387—61no—
94#387—61no—
95#385—61no—
96#380—31no—
97C4×C22⋊C4—61no—
98C2×#95—31no—
99C2×#95—61no—
100C2×#95—61no—
101C2×#95C2×D311yescharacteristic
102#340—61no—
103#340—61no—
104#328—22no—
105C24×C3C2×D411yescharacteristic
106C2×C3×Q8—21no—
107C2×C3×Q8—41no—
108C2×C3×Q8—41no—
109C2×C3×Q8C22⋊C412yes—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—22no—
113C22×C3×C4—41no—
114C22×C3×C4—41no—
115C22×C3×C4—41no—
116C22×C3×C4—41no—
117C22×C3×C4—41no—
118C22×C3×C4—41no—
119C22×C3×C4—41no—
120C22×C3×C4—41no—
121C22×C3×C4C22×C411yescharacteristic
122C22×C3×C4C2×D411yescharacteristic
123C22×C3×C4C2×D411yescharacteristic
124C22×C3×C4C2×D411yescharacteristic
125C22×C3×C4#4111yescharacteristic
126C22×C3×C4#4111yescharacteristic
127C22×Dic3—21no—
128C22×Dic3—21no—
129C22×Dic3—22no—
130C22×Dic3—21no—
131C22×Dic3—21no—
132C22×Dic3—21no—
133C22×Dic3—21no—
134C22×Dic3—21no—
135C22×Dic3—41no—
136C22×Dic3—41no—
137C22×Dic3—41no—
138C22×Dic3—41no—
139C22×Dic3—41no—
140C22×Dic3—41no—
141C22×Dic3—41no—
142C22×Dic3—41no—
143C22×Dic3—41no—
144C22×Dic3—41no—
145C22×Dic3SD1612yes—
146C2×C3×C8—41no—
147C2×C3×C8—41no—
148C2×C3×C8—41no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4C22⋊C412yes—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155#217—41no—
156#217—41no—
157C4⋊Dic3—22no—
158C4⋊Dic3—22no—
159C4⋊Dic3—41no—
160C4⋊Dic3—41no—
161C4⋊Dic3—41no—
162C4⋊Dic3—41no—
163C4⋊Dic3—81no—
164C4⋊Dic3—81no—
165C4×Dic3—81no—
166C4×Dic3—81no—
167C2×C3⋊C8—22no—
168C2×C3⋊C8—41no—
169C2×C3⋊C8—41no—
170C22×Q8D1211yescharacteristic
171C23×C4—21no—
172C23×C4—31no—
173C23×C4—31no—
174C23×C4—61no—
175C23×C4C22×D311yescharacteristic
176C22×C8—21no—
177C22×C8—61no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C22⋊Q8C4×D312yes—
181C22⋊Q8#6712yes—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—32no—
184C2×C4⋊C4—31no—
185C2×C4⋊C4—31no—
186C2×C4⋊C4—61no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4—61no—
189C2×C4⋊C4—61no—
190C2×C4⋊C4—61no—
191C2×C4⋊C4—61no—
192C2×C4⋊C4—61no—
193C2×C4⋊C4D1211yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—61no—
196C2×C42—61no—
197C2×C42—61no—
198#106—64no—
199#103—64no—
200C22⋊C8—21no—
201C22⋊C8—21no—
202C22⋊C8—32no—
203C22⋊C8—61no—
204#95—21no—
205#95—21no—
206#95—61no—
207#95—61no—
208#95—61no—
209#95—61no—
210#95—61no—
211#95—61no—
212#95—61no—
213#95—122no—
214#95—122no—
215C23×C3—21no—
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3C4×D411yescharacteristic
220C23×C3#12011yescharacteristic
221C23×C3#12111yescharacteristic
222C23×C3C2×SD1611yescharacteristic
223C23×C3#13511yescharacteristic
224C23×C3AGL(1,ℤ/8)11yescharacteristic
225C23×C3#13711yescharacteristic
226C3×Q8—42no—
227C3×Q8—81no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—81no—
246C2×C3×C4—81no—
247C2×C3×C4—81no—
248C2×C3×C4—81no—
249C2×C3×C4C2×C22⋊C411yescharacteristic
250C2×C3×C4C4×D411yescharacteristic
251C2×C3×C4#12111yescharacteristic
252C2×C3×C4#12311yescharacteristic
253C2×Dic3—22no—
254C2×Dic3—41no—
255C2×Dic3—41no—
256C2×Dic3—42no—
257C2×Dic3—42no—
258C2×Dic3—42no—
259C2×Dic3—42no—
260C2×Dic3—42no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—41no—
264C2×Dic3—41no—
265C2×Dic3—41no—
266C2×Dic3—41no—
267C2×Dic3—41no—
268C2×Dic3—41no—
269C2×Dic3—41no—
270C2×Dic3—81no—
271C2×Dic3—81no—
272C2×Dic3—81no—
273C2×Dic3—81no—
274C2×Dic3—81no—
275C2×Dic3—81no—
276C3×C8—81no—
277C3⋊C8—42no—
278C24D3×D411yescharacteristic
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8(C2×D3)⋊C412yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—32no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—61no—
296C22×C4—61no—
297C22×C4—62no—
298C22×C4—61no—
299C22×C4—61no—
300C22×C4—61no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4—121no—
304C22×C4—121no—
305C22×C4—121no—
306C22×C4—121no—
307C22×C4—121no—
308C22×C4—121no—
309C22×C4—121no—
310C22×C4—121no—
311C22×C4—121no—
312C22×C4—121no—
313C22×C4C2×C4×D311yescharacteristic
314C22×C4C2×D1211yescharacteristic
315C22×C4D3×D411yescharacteristic
316C22×C4#23711yescharacteristic
317C22×C4#23711yescharacteristic
318C22×C4C2×#6711yescharacteristic
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—62no—
323C2×C8—121no—
324C2×C8—121no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—62no—
329C4⋊C4—62no—
330C4⋊C4—121no—
331C4⋊C4—121no—
332C4⋊C4—121no—
333C4⋊C4—121no—
334C4⋊C4—241no—
335C4⋊C4—241no—
336C4⋊C4(C2×D3)⋊C412yes—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—121no—
340C22⋊C4—121no—
341C42—241no—
342C42—241no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3#38611yescharacteristic
356C22×C3C4×SD1611yescharacteristic
357C22×C3#44011yescharacteristic
358C22×C3#44811yescharacteristic
359C22×C3#44911yescharacteristic
360C22×C3#45511yescharacteristic
361C22×C3#45611yescharacteristic
362C22×C3#45811yescharacteristic
363C22×C3#45811yescharacteristic
364C22×C3#46011yescharacteristic
365C22×C3#46411yescharacteristic
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—82no—
373Dic3—42no—
374Dic3—81no—
375Dic3—81no—
376Dic3—81no—
377Dic3—82no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23#67⋊C411yescharacteristic
383C23#88211yescharacteristic
384C23D3×SD1611yescharacteristic
385C23#91411yescharacteristic
386C23#91811yescharacteristic
387C23#91911yescharacteristic
388C23#93911yescharacteristic
389Q8—42no—
390Q8—81no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—62no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—121no—
414C2×C4—121no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—122no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—122no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—241no—
430C2×C4—241no—
431C2×C4—241no—
432C2×C4—241no—
433C2×C4—241no—
434C2×C4—241no—
435C2×C4#67⋊C411yescharacteristic
436C2×C4#88611yescharacteristic
437C2×C4C2×(C2×D3)⋊C411yescharacteristic
438C2×C4#93911yescharacteristic
439C8—81no—
440C8—122no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3#160811yescharacteristic
446C2×C3#160911yescharacteristic
447C2×C3#161111yescharacteristic
448C2×C3#161211yescharacteristic
449C2×C3#188011yescharacteristic
450C2×C3#188211yescharacteristic
451C2×C3#189011yescharacteristic
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22#474211yescharacteristic
465C22#474211yescharacteristic
466C22#478811yescharacteristic
467C22#480611yescharacteristic
468C22#481011yescharacteristic
469C22#481711yescharacteristic
470C22#482511yescharacteristic
471C22#482611yescharacteristic
472C22#495811yescharacteristic
473C22#516311yescharacteristic
474C22#518511yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—82no—
482C4—122no—
483C4—242no—
484C4—241no—
485C4—241no—
486C4—241no—
487C3#904411yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—21no—
491C2—21no—
492C2#6832011yescharacteristic
493C2#6832111yescharacteristic
494C2#6832811yescharacteristic
495C2#6832911yescharacteristic
496C2#7002311yescharacteristic
497C2#7024011yescharacteristic
498C2#7036511yescharacteristic
subgroupG/H
centerC23#882
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#328C2
socleC23×C3#120
prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenterC2×#328D3
hypocenterC3#9044
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
21. #5043C4semidirect
487. C3#9044semidirect

Maximal subgroups

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

subgroupindex
#827452
C2×#50432
C2×C3×#3282
#699242
#694232
#676742
#676122
#90443