Finite Group Databasebeta

← #11870816

Subgroups — #11870816

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×Dic6C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic, complemented
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4833C211yesmaximal, characteristic
6#10590952C212yesmaximal
7#10590807C212yesmaximal, complemented
8#10590793C212yesmaximal, complemented
9#10590684C212yesmaximal
10#10590385C211yesmaximal, characteristic, complemented
11#10590284C211yesmaximal, characteristic, complemented
12#81092—31nomaximal
13#79310—31nomaximal
14C2×D3×Dic6C2211yescharacteristic
15C2×#3746C2212yes—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4×#627—21no—
22D3×C4⋊Dic3C2211yescharacteristic
23D3×Dic3⋊C4—21no—
24C4×D3×Dic3—21no—
25#63869—21no—
26#63857C2212yes—
27#63856—21no—
28#63844C2212yes—
29#63844C2211yescharacteristic
30Dic3×Dic6—21no—
31Dic3×Dic6C2211yescharacteristic
32#63841—21no—
33#63837—21no—
34C2×#3719C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36#63643C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×#818C2212yes—
39C3×#816C2212yes—
40C3×C8×Dic3C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63575C2212yes—
43#63567C2212yes—
44#63567C2212yes—
45#5728—31no—
46C4×D3×Q8—31no—
47#5470—31no—
48C2×C4×Dic6—31no—
49C3×#477—31no—
50C3×#431—31no—
51#5091—31no—
52#5031—31no—
53#4884—32no—
54#4873—32no—
55#4850—31no—
56#4850D311yescharacteristic, complemented
57#4849—31no—
58#4849—31no—
59#4849—31no—
60#4849—61no—
61#4833D311yescharacteristic
62#4809—32no—
63#4790—32no—
64#4739—32no—
65#4722—32no—
66C4×Dic12—32no—
67C4×Dic12—32no—
68C2×#634C2312yes—
69C2×#634C2311yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78D3×Dic6—22no—
79D3×Dic6—22no—
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86C4×C3⋊Dic3—21no—
87#3746—24no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3D411yescharacteristic
95C3×C4×Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3724—22no—
98#3724—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—21no—
102(C2×D3)⋊Dic3—22no—
103Dic32—21no—
104Dic32—21no—
105Dic32—22no—
106#3719—24no—
107#3104—91noSylow
108C2×D3×Q8—31no—
109C22×Dic6—31no—
110C3×C4⋊Q8—31no—
111C3×C4×Q8—31no—
112C2×C3×C42—31no—
113#946—61no—
114Q8×Dic3—31no—
115Q8×Dic3—61no—
116C2×#216—32no—
117#926—61no—
118C2×C4⋊Dic3—31no—
119#924—32no—
120#924—61no—
121C2×Dic3⋊C4—61no—
122C2×C4×Dic3—61no—
123C2×Dic12—32no—
124C2×Dic12—32no—
125C2×Dic12—32no—
126C2×Dic12—62no—
127#897—32no—
128#892—61no—
129D3×C4⋊C4—31no—
130D3×C4⋊C4—61no—
131#890—61no—
132#887—31no—
133#887—32no—
134#887—61no—
135C42×D3—61no—
136C42×D3C2×D311yescharacteristic
137#870—61no—
138#869—31no—
139#869—31no—
140#869—61no—
141#869C2×D311yescharacteristic
142C4×Dic6—31no—
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—31no—
146C4×Dic6—32no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C4×Dic6—61no—
150C4×Dic6—61no—
151C4×Dic6—61no—
152C4×Dic6C2×D311yescharacteristic
153C3×#107—32no—
154C3×C4⋊C8—21no—
155C3×C4⋊C8—31no—
156C3×C4⋊C8C2×D311yescharacteristic
157C3×C4⋊C8C2×D311yescharacteristic
158C3×#103—32no—
159C3×C22⋊C8—32no—
160C3×C4×C8—32no—
161(C2×D3)⋊C8C2×D312yes—
162#818—32no—
163#818C2×D312yes—
164#816—32no—
165#816—32no—
166#816—32no—
167#816—32no—
168#816—62no—
169#816C2×D312yes—
170C8×Dic3C2×D312yes—
171#810—32no—
172#810—32no—
173#807—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3×D3C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—21no—
182#634—21no—
183#634—22no—
184#634—22no—
185#634#4112yes—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×C4×D3—21no—
193C3×C4×D3—21no—
194C3×C4×D3—41no—
195C3×C4×D3Q1614yescomplemented
196C3×Dic6—21no—
197C3×Dic6—42no—
198C3×Dic6#4112yes—
199#627—24no—
200D3×Dic3—24no—
201D3×Dic3—42no—
202C32×C8—22no—
203C3×C3⋊C8—22no—
204#533—91no—
205C2×C4×Q8—91no—
206#484—92no—
207#477—31no—
208#477—91no—
209#462—91no—
210#462—91no—
211#451—92no—
212C4×Q16—92no—
213C4×Q16—92no—
214#431—31no—
215C2×C3×Q8—31no—
216C2×C3×Q8—61no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222D3×Q8—62no—
223D3×Q8—62no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3D1211yescharacteristic
227C2×C4×D3D1211yescharacteristic
228C2×C4×D3C22×D311yescharacteristic
229C2×Dic6—21no—
230C2×Dic6—31no—
231C2×Dic6—31no—
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—61no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—62no—
240C2×Dic6C22×D311yescharacteristic
241C2×C3×C8—22no—
242C2×C3×C8—32no—
243C2×C3×C8C22×D312yes—
244C2×C3×C8C22×D312yes—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C42—21no—
250C3×C42—31no—
251C3×C42—31no—
252C3×C42—31no—
253C3×C42—61no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#216—64no—
258(C2×D3)⋊C4—62no—
259C4⋊Dic3—21no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—62no—
270C4⋊Dic3—121no—
271C4⋊Dic3—121no—
272C4⋊Dic3C22×D311yescharacteristic
273C4⋊Dic3C22×D312yes—
274Dic3⋊C4—21no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—62no—
284Dic3⋊C4—121no—
285C4×Dic3—21no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—62no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—62no—
294C4×Dic3—121no—
295C4×Dic3D1211yescharacteristic
296C4×Dic3D1211yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298C2×C3⋊C8C22×D312yes—
299Dic12—64no—
300Dic12—64no—
301Dic12—64no—
302Dic12—124no—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3—21no—
305C2×C3×D3—21no—
306C2×C3×D3C2×Q1612yes—
307C32×C4—21no—
308C32×C4C2×Q1612yes—
309C32×C4C2×#4111yescharacteristic
310C32×C4C2×#4111yescharacteristic
311C3⋊Dic3—22no—
312C3⋊Dic3—42no—
313C3⋊Dic3—41no—
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3—21no—
317C3×Dic3—41no—
318C3×Dic3—42no—
319C3×Dic3C2×Q1612yes—
320C22×Q8—91no—
321C2×Q16—92no—
322C2×Q16—92no—
323C4⋊Q8—31no—
324C4⋊Q8—91no—
325#125—181no—
326C22⋊Q8—92no—
327C22⋊Q8—181no—
328C4×Q8—31no—
329C4×Q8—91no—
330C4×Q8—92no—
331C4×Q8—91no—
332C4×Q8—91no—
333C4×Q8—181no—
334C4×Q8—181no—
335C4×Q8—181no—
336#117—181no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4—181no—
339C2×C42—31no—
340C2×C42—181no—
341#107—32no—
342#107—92no—
343C4⋊C8—31no—
344C4⋊C8D3211yescharacteristic
345#103—32no—
346#103—92no—
347#103—92no—
348#103—92no—
349C22⋊C8—32no—
350C4×C8—32no—
351C23×C3—31no—
352C22×D3C2×D1211yescharacteristic
353C3×Q8—32no—
354C3×Q8—61no—
355C3×Q8—122no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—31no—
360C2×C3×C4—34no—
361C2×C3×C4—31no—
362C2×C3×C4—31no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—121no—
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—64no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—62no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3C2×D1211yescharacteristic
390C2×Dic3C2×D1211yescharacteristic
391C2×Dic3C2×D1211yescharacteristic
392C4×D3—21no—
393C4×D3—21no—
394C4×D3—41no—
395C4×D3—64no—
396C4×D3—122no—
397C4×D3Dic1214yescomplemented
398Dic6—21no—
399Dic6—32no—
400Dic6—32no—
401Dic6—42no—
402Dic6—62no—
403Dic6—64no—
404Dic6—64no—
405Dic6—61no—
406Dic6—61no—
407Dic6—62no—
408Dic6—62no—
409Dic6—62no—
410Dic6—62no—
411Dic6—121no—
412Dic6—122no—
413Dic6—122no—
414Dic6#23912yes—
415C3×C8—22no—
416C3×C8—22no—
417C3×C8—42no—
418C3×C8—62no—
419C3⋊C8—22no—
420C2×C32#52511yescharacteristic
421C2×C32C22×Q1611yescharacteristic
422C2×C32#57511yescharacteristic
423C3×D3—22no—
424C2×Q8—31no—
425C2×Q8—61no—
426C2×Q8—91no—
427C2×Q8—92no—
428C2×Q8—181no—
429C2×Q8—182no—
430C2×Q8—182no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—181no—
435C22×C4—181no—
436Q16—184no—
437Q16—184no—
438C2×C8—32no—
439C2×C8C2×D3212yes—
440C4⋊C4—32no—
441C4⋊C4—31no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—91no—
445C4⋊C4—181no—
446C4⋊C4—181no—
447C4⋊C4—181no—
448C4⋊C4—182no—
449C4⋊C4—182no—
450C4⋊C4—181no—
451C4⋊C4—181no—
452C4⋊C4—181no—
453C22⋊C4—182no—
454C42—31no—
455C42—31no—
456C42—31no—
457C42—61no—
458C42—181no—
459C42—181no—
460C42—182no—
461C42—181no—
462C42C2×D3211yescharacteristic
463C22×C3—21no—
464C22×C3—32no—
465C22×C3—61no—
466C22×C3—61no—
467C22×C3C22×D1211yescharacteristic
468C22×C3C2×D3×D411yescharacteristic
469C2×D3—21no—
470C2×D3—21no—
471C2×D3C2×Dic1212yes—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—32no—
478C3×C4—41no—
479C3×C4—61no—
480C3×C4—62no—
481C3×C4—61no—
482C3×C4—121no—
483C3×C4—122no—
484C3×C4C2×Dic1212yes—
485C3×C4D3×Q1612yes—
486C3×C4C2×#23911yescharacteristic
487C3×C4D3×#4111yescharacteristic
488C3×C4D3×#4111yescharacteristic
489C3×C4D3×#4111yescharacteristic
490Dic3—21no—
491Dic3—21no—
492Dic3—22no—
493Dic3—42no—
494Dic3—41no—
495Dic3—62no—
496Dic3—62no—
497Dic3—122no—
498Dic3—121no—
499Dic3—121no—
500Dic3—122no—
501Dic3—122no—
502Dic3—242no—
503Dic3—241no—
504Dic3C2×Dic1212yes—
505C32#310411yescharacteristic, complemented, Sylow
506C23—31no—
507Q8—32no—
508Q8—61no—
509Q8—92no—
510Q8—122no—
511Q8—184no—
512Q8—181no—
513Q8—182no—
514Q8—182no—
515C2×C4—31no—
516C2×C4—34no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—121no—
525C2×C4—184no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—182no—
529C2×C4—362no—
530C2×C4D3×D1211yescharacteristic
531C2×C4D3×D1211yescharacteristic
532C2×C4C22×D3211yescharacteristic
533C8—22no—
534C8—62no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—62no—
539C2×C3#552411yescharacteristic
540C2×C3#562711yescharacteristic
541C2×C3C22×Dic1211yescharacteristic
542C2×C3#574811yescharacteristic
543C2×C3C2×D3×Q1611yescharacteristic
544C2×C3#577311yescharacteristic
545D3—22no—
546C22—32no—
547C22—61no—
548C22—61no—
549C22C2×D3×D1211yescharacteristic
550C4—21no—
551C4—32no—
552C4—61no—
553C4—62no—
554C4—61no—
555C4—121no—
556C4—122no—
557C4—182no—
558C4—362no—
559C4—361no—
560C4D3×Dic1212yes—
561C4#6431211yescharacteristic
562C4D3×#23911yescharacteristic
563C3—21no—
564C3#7931011yescharacteristic, complemented
565C3#8109211yescharacteristic, complemented
566C2—62no—
567C2#1059462711yescharacteristic
568C2C2×D3×Dic1211yescharacteristic
569C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592548C2semidirect
4. C3×#4850C2semidirect
7. #10590807C2semidirect
8. #10590793C2semidirect
10. #10590385C2semidirect
11. #10590284C2semidirect
56. #4850D3semidirect
195. C3×C4×D3Q16semidirect
397. C4×D3Dic12semidirect
505. C32#3104semidirect
564. C3#79310semidirect
565. C3#81092semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Dic62
#105938592
#105925482
C3×#48502
C3×#48332
#105909522
#105908072
#105907932
#105906842
#105903852
#105902842
#810923
#793103