Finite Group Databasebeta

← #11791489

Subgroups — #11791489

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63864C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic
3C2×C3×#816C211yesmaximal, characteristic, complemented
4C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
5Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#70458—31nomaximal
9#70230—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—21no—
18C2×#3722—21no—
19C2×Dic32—21no—
20#63864—22no—
21#63864C414yescomplemented
22#63648—22no—
23C3×#816—22no—
24C3×Dic3⋊C8—22no—
25#63579—21no—
26#63566—22no—
27#63564—22no—
28C2×#947—31no—
29C2×#875—31no—
30C2×C3×C4⋊C8—31no—
31C2×C3×#103—31no—
32C2×#835—31no—
33C2×#821—31no—
34C2×#821—31no—
35C2×#821—31no—
36C2×#821—61no—
37C2×#816—31no—
38C2×#816D311yescharacteristic, complemented
39C2×Dic3⋊C8D311yescharacteristic, complemented
40Dic3×C4⋊C4—31no—
41C2×#809—31no—
42C4×C4⋊Dic3—31no—
43C23×C3⋊D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D412yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×C4×Dic3C2×C412yes—
70C3×C4×Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3722—24no—
75#3722—24no—
76Dic32—42no—
77#1983—91noSylow
78C22×C3×Q8—31no—
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C42—31no—
89#947—34no—
90#947—62no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4×Dic3—61no—
100C2×C4×Dic3—61no—
101C2×C4×Dic3C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103#875—34no—
104#875—62no—
105C3×C4⋊C8—62no—
106C3×#103—62no—
107#835—62no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110#821—62no—
111#821—62no—
112#821—64no—
113#821—62no—
114#816—22no—
115#816—62no—
116Dic3⋊C8—22no—
117#809—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—41no—
138C4⋊(C3⋊D3)—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3C22⋊C412yes—
150C2×C3×Dic3C22⋊C412yes—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157C2×#124—91no—
158C2×C4⋊C8—31no—
159C2×#103—31no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#102—91no—
163C4×C4⋊C4—91no—
164C23×D3—61no—
165C23×D3—61no—
166C23×D3—121no—
167C2×C3×Q8—32no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3D1211yescharacteristic
186C22×Dic3D1211yescharacteristic
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—121no—
203C2×D12—121no—
204C2×D12—121no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C4×D312yes—
211C2×C3×C8—22no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—41no—
219C2×C3×C8—41no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C42—32no—
226C3×C42—32no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231C4⋊Dic3—21no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—62no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—121no—
238C4⋊Dic3#6712yes—
239C4×Dic3—122no—
240C4×Dic3—122no—
241C4×Dic3C4×D312yes—
242C4×Dic3#6712yes—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C22×C32C2×C22⋊C411yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32#12111yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C22×C32#13711yescharacteristic
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—81no—
257C2×C3⋊D3—81no—
258C2×C3⋊D3—81no—
259C2×C3⋊D3—81no—
260C32×C4C4×D411yescharacteristic
261C32×C4C4×D411yescharacteristic
262C32×C4#12411yescharacteristic
263C32×C4#12711yescharacteristic
264C3⋊Dic3—42no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C22×Q8—31no—
270C22×D4—91no—
271C22×C8—31no—
272C22×C8D3211yescharacteristic
273#124—94no—
274#124—182no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—91no—
277C2×C22⋊C4—181no—
278C2×C22⋊C4—181no—
279C2×C42—31no—
280C2×C42—181no—
281C4⋊C8—62no—
282#103—62no—
283#103—182no—
284#102—182no—
285#102—182no—
286#95—181no—
287C23×C3—21no—
288C23×C3C2×D1211yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—241no—
308C22×D3—241no—
309C22×D3—241no—
310C22×D3—241no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—121no—
314C3×Q8—121no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—241no—
363C2×Dic3—241no—
364C2×Dic3(C2×D3)⋊C412yes—
365C2×Dic3(C2×D3)⋊C412yes—
366D12—64no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—62no—
371D12—122no—
372D12—122no—
373D12—122no—
374D12—121no—
375D12—121no—
376D12—121no—
377D12—121no—
378Dic6—22no—
379Dic6—22no—
380Dic6—41no—
381Dic6—41no—
382C3×C8—42no—
383C3×C8—41no—
384C3×C8—41no—
385C3×C8—121no—
386C3⋊C8—41no—
387C2×C32#39011yescharacteristic
388C2×C32#41611yescharacteristic
389C2×C32#41711yescharacteristic
390C2×C32#46311yescharacteristic
391C2×C32#46311yescharacteristic
392C2×C32#46411yescharacteristic
393C2×C32#46411yescharacteristic
394C3⋊D3—82no—
395C24—181no—
396C2×Q8—32no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C2×Q8—61no—
402C2×D4—92no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4—181no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—181no—
413C22×C4C2×D3211yescharacteristic
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C4⋊C4—32no—
421C4⋊C4—61no—
422C4⋊C4—92no—
423C4⋊C4—181no—
424C22⋊C4—184no—
425C22⋊C4—184no—
426C42—32no—
427C42—32no—
428C42—362no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3D3×C22⋊C411yescharacteristic
437C22×C3#88411yescharacteristic
438C22×C3#89511yescharacteristic
439C22×C3#89511yescharacteristic
440C22×C3#90411yescharacteristic
441C22×C3#90411yescharacteristic
442C22×C3#90811yescharacteristic
443C22×C3#90911yescharacteristic
444C22×C3#91411yescharacteristic
445C22×C3#91611yescharacteristic
446C22×C3#91811yescharacteristic
447C22×C3#91911yescharacteristic
448C22×C3C2×(C2×D3)⋊C411yescharacteristic
449C22×C3#93911yescharacteristic
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—242no—
458C2×D3—242no—
459C2×D3—242no—
460C2×D3—242no—
461C2×D3—242no—
462C2×D3—242no—
463C2×D3—241no—
464C2×D3—241no—
465C2×D3—241no—
466C2×D3—241no—
467C2×D3—241no—
468C2×D3—241no—
469C2×D3—241no—
470C2×D3—241no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4—122no—
478C3×C4—122no—
479C3×C4#67⋊C411yescharacteristic
480C3×C4#88511yescharacteristic
481C3×C4#89311yescharacteristic
482C3×C4#89311yescharacteristic
483C3×C4C4×#6711yescharacteristic
484C3×C4#94011yescharacteristic
485C3×C4#94011yescharacteristic
486C3×C4#94711yescharacteristic
487Dic3—22no—
488Dic3—22no—
489Dic3—42no—
490Dic3—42no—
491Dic3—122no—
492Dic3—122no—
493Dic3—242no—
494C32#198311yescharacteristic, complemented, Sylow
495C23—182no—
496C23—361no—
497C23—361no—
498C23—361no—
499C23—361no—
500C23—361no—
501C23—361no—
502C23D3×D1211yescharacteristic
503Q8—62no—
504Q8—62no—
505Q8—121no—
506Q8—121no—
507D4—182no—
508D4—182no—
509D4—361no—
510D4—361no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—121no—
523C2×C4—182no—
524C2×C4—361no—
525C2×C4—361no—
526C2×C4#379611yescharacteristic
527C2×C4#379911yescharacteristic
528C2×C4C4×D3211yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4D3×#6711yescharacteristic
531C2×C4#381111yescharacteristic
532C8—41no—
533C8—121no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3#479811yescharacteristic
542C2×C3#480311yescharacteristic
543C2×C3#480411yescharacteristic
544C2×C3#481911yescharacteristic
545C2×C3#484411yescharacteristic
546C2×C3#484411yescharacteristic
547C2×C3#484511yescharacteristic
548C2×C3#484511yescharacteristic
549C2×C3#495711yescharacteristic
550C2×C3#498811yescharacteristic
551C2×C3#511311yescharacteristic
552C2×C3#513311yescharacteristic
553C2×C3#516511yescharacteristic
554C2×C3#518511yescharacteristic
555D3—244no—
556D3—242no—
557D3—242no—
558C22—362no—
559C22—362no—
560C22—362no—
561C22—721no—
562C22—721no—
563C22—721no—
564C22—721no—
565C22#6379411yescharacteristic
566C22#6380111yescharacteristic
567C22#6380611yescharacteristic
568C22#6380811yescharacteristic
569C22#6388611yescharacteristic
570C22#6391011yescharacteristic
571C22D3×(C2×D3)⋊C411yescharacteristic
572C4—62no—
573C4—62no—
574C4—122no—
575C4—122no—
576C4—362no—
577C4#6388111yescharacteristic
578C4#6390411yescharacteristic
579C4#6390711yescharacteristic
580C4#6397911yescharacteristic
581C3—21no—
582C3#7023011yescharacteristic, complemented
583C3#7045811yescharacteristic, complemented
584C2—722no—
585C2#1059067111yescharacteristic
586C2#1059069011yescharacteristic
587C2#1059075411yescharacteristic
588C2#1059077011yescharacteristic
589C2#1059080111yescharacteristic
590C2#1059081311yescharacteristic
591C2#1059138411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1983
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#816C2semidirect
4. C2×C3×Dic3⋊C8C2semidirect
5. Dic3×C4⋊Dic3C2semidirect
6. C2×#63566C2semidirect
21. #63864C4semidirect
38. C2×#816D3semidirect
39. C2×Dic3⋊C8D3semidirect
494. C32#1983semidirect
582. C3#70230semidirect
583. C3#70458semidirect

Maximal subgroups

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

subgroupindex
C2×#638642
C2×#636482
C2×C3×#8162
C2×C3×Dic3⋊C82
Dic3×C4⋊Dic32
C2×#635662
C2×#635642
#704583
#702303