Finite Group Databasebeta

← #11787742

Subgroups — #11787742

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic, complemented
2C2×#63823C211yesmaximal, characteristic
3C3×#4939C211yesmaximal, characteristic, complemented
4C2×C3×#805C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6#10589389C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70366—31nomaximal
9#69663—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18Dic3×#67—22no—
19#63898—21no—
20D3×C4⋊Dic3—21no—
21#63843—21no—
22#63841—21no—
23C2×#3715—21no—
24#63823—22no—
25#63823C414yescomplemented
26C2×#3713—21no—
27C3×#805—22no—
28#63563—21no—
29#63563—21no—
30#5827—31no—
31C2×#949—31no—
32C2×#932—31no—
33#5504—31no—
34C2×C3×#104—31no—
35C3×#390—31no—
36#5215—31no—
37#5131—31no—
38#4939D311yescharacteristic, complemented
39C2×#805D311yescharacteristic, complemented
40#4554—31no—
41#4530—31no—
42#4523—31no—
43#4523—31no—
44#4523—61no—
45C23×C3×D3—21no—
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—21no—
49C22×C3×Dic3D412yes—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235C2×C412yes—
53C3×#235D412yes—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×C42—21no—
65C32×C42—21no—
66#3757—21no—
67C4⋊(C3⋊Dic3)D411yescharacteristic
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4×C3⋊Dic3—21no—
70#3748—21no—
71#3748C2×C412yescomplemented
72C2×C3⋊(C3⋊C8)—21no—
73C3×(C2×D3)⋊C4—44no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79Dic3⋊Dic3—22no—
80(C2×D3)⋊Dic3—22no—
81Dic32—22no—
82#3715—24no—
83#3713—24no—
84#1883—91noSylow
85C2×C3×#41—31no—
86C22×C3×D4—31no—
87C2×#235C2×D311yescharacteristic
88C22×D12C2×D311yescharacteristic
89C2×C3×M16—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—62no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95#949—34no—
96#949—62no—
97Q8×Dic3—61no—
98C2×#215—61no—
99D4×Dic3—61no—
100D4×Dic3—62no—
101C2×#214—61no—
102#932—34no—
103#932—62no—
104C2×#213—61no—
105C2×#213—61no—
106C4×#67—62no—
107C2×(C2×D3)⋊C4—22no—
108#926—31no—
109#926—31no—
110#926—61no—
111#926—61no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—61no—
117C2×#208C2×D311yescharacteristic
118#893—61no—
119#892—61no—
120D3×C4⋊C4—61no—
121#887—61no—
122C3×#104—62no—
123#832—61no—
124#832—61no—
125#821—61no—
126#821—61no—
127#805—22no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—21no—
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C3×#67—22no—
147C3×#67—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—42no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—21no—
154C3×D12—41no—
155C3×D12—41no—
156C3×D12C22⋊C412yescomplemented
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×Dic6—21no—
160C3×Dic6C22⋊C412yescomplemented
161D3×Dic3—82no—
162C3⋊(C3⋊C8)—22no—
163C3×C3⋊C8—41no—
164C2×AGL(1,ℤ/8)—91no—
165#520—91no—
166C2×#104—31no—
167#418—91no—
168#390—31no—
169#343—91no—
170#339—91no—
171C24×C3—61no—
172C23×D3—21no—
173C3×#41—32no—
174C3×#41—32no—
175C3×#41—61no—
176C3×#41—61no—
177C2×C3×Q8—31no—
178C2×C3×D4—32no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—32no—
190C22×C3×C4—41no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—21no—
195C22×Dic3—62no—
196C22×Dic3#6712yes—
197#235—21no—
198#235—21no—
199#235C4×D312yes—
200#235#6712yes—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12C4×D312yescomplemented
207C2×D12D1211yescharacteristic
208C2×C4×D3—21no—
209C2×C4×D3—62no—
210C2×Dic6D1211yescharacteristic
211C3×M16—61no—
212C3×M16—61no—
213C2×C3×C8—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C22⋊C4—124no—
217C3×C42—22no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—41no—
223#217—62no—
224#217—61no—
225#217—61no—
226#217—121no—
227#215—64no—
228#214—64no—
229#213—64no—
230#213—64no—
231(C2×D3)⋊C4—44no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—62no—
242Dic3⋊C4—62no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—121no—
248#208—21no—
249#208—21no—
250#208—32no—
251#208—32no—
252#208—62no—
253#208—61no—
254#208—61no—
255#208—121no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32C4×D411yescharacteristic
263C22×C32#12011yescharacteristic
264C22×C32#12111yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—41no—
267C2×C3×D3—41no—
268C2×C3×D3—44no—
269C2×C3×D3—42no—
270C2×C3×D3—82no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C32×C4—42no—
274C32×C4C2×C22⋊C411yescharacteristic
275C32×C4C4×D411yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12311yescharacteristic
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—42no—
282C2×#41—31no—
283C22×D4—31no—
284AGL(1,ℤ/8)—94no—
285AGL(1,ℤ/8)—182no—
286C2×SD16—181no—
287C2×D8—181no—
288C2×M16—31no—
289C2×M16—91no—
290C4×Q8—181no—
291C4×D4—181no—
292C4×D4—182no—
293#117—91no—
294#117—181no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—181no—
297C2×C22⋊C4—62no—
298C2×C42D3211yescharacteristic
299#104—62no—
300#102—181no—
301#102—181no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3—62no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—21no—
312C22×D3—22no—
313C22×D3—42no—
314C22×D3—42no—
315C22×D3—41no—
316C22×D3—41no—
317C3×Q8—32no—
318C3×Q8—61no—
319C3×D4—32no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—61no—
324C3×D4—62no—
325C3×D4—121no—
326C3×D4—121no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—22no—
360#67—22no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—42no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—242no—
371D12—22no—
372D12—22no—
373D12—21no—
374D12—41no—
375D12—41no—
376D12(C2×D3)⋊C412yescomplemented
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—242no—
380Dic6—21no—
381Dic6(C2×D3)⋊C412yescomplemented
382C3×C8—121no—
383C3⋊C8—41no—
384C3⋊C8—62no—
385C3⋊C8—62no—
386C3⋊C8—122no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32#38611yescharacteristic
390C2×C32#45311yescharacteristic
391C2×C32#45411yescharacteristic
392C3×D3—42no—
393C3×D3—82no—
394C24—61no—
395#41—32no—
396#41—32no—
397#41—61no—
398#41—61no—
399C2×Q8—31no—
400C2×D4—32no—
401C2×D4—31no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C22×C4—21no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4—182no—
412C22×C4C2×D3211yescharacteristic
413SD16—184no—
414D8—184no—
415M16—61no—
416M16—61no—
417M16—92no—
418M16—181no—
419C2×C8—61no—
420C2×C8—181no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C22⋊C4—124no—
427C22⋊C4—182no—
428C22⋊C4—181no—
429C42—21no—
430C42—21no—
431C42—182no—
432C42—181no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—62no—
443C22×C3—124no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3—242no—
448C22×C3—241no—
449C22×C3—241no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3C4×#6711yescharacteristic
453C22×C3#93711yescharacteristic
454C22×C3#93811yescharacteristic
455C22×C3#93911yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—44no—
460C2×D3—42no—
461C2×D3—82no—
462C2×D3—81no—
463C2×D3—81no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—44no—
471C3×C4—62no—
472C3×C4—122no—
473C3×C4D3×C22⋊C411yescharacteristic
474C3×C4#67⋊C411yescharacteristic
475C3×C4#67⋊C411yescharacteristic
476C3×C4#88311yescharacteristic
477C3×C4#88411yescharacteristic
478C3×C4#88611yescharacteristic
479C3×C4C2×(C2×D3)⋊C411yescharacteristic
480C3×C4#93911yescharacteristic
481Dic3—22no—
482Dic3—42no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—241no—
488Dic3—241no—
489C32#188311yescharacteristic, complemented, Sylow
490C23—61no—
491C23—62no—
492C23—122no—
493C23—122no—
494C23—121no—
495C23—121no—
496C23D3×#6711yescharacteristic
497Q8—32no—
498Q8—61no—
499D4—32no—
500D4—62no—
501D4—62no—
502D4—61no—
503D4—62no—
504D4—62no—
505D4—121no—
506D4—121no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—122no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—722no—
518C2×C4#379511yescharacteristic
519C2×C4C4×D3211yescharacteristic
520C2×C4D3×D1211yescharacteristic
521C2×C4#380211yescharacteristic
522C2×C4#380511yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C8—121no—
525C8—182no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—122no—
536C2×C3—242no—
537C2×C3#482211yescharacteristic
538C2×C3#482711yescharacteristic
539C2×C3#495611yescharacteristic
540C2×C3#495811yescharacteristic
541C2×C3#506211yescharacteristic
542C2×C3#507711yescharacteristic
543D3—42no—
544D3—82no—
545C22—21no—
546C22—21no—
547C22—62no—
548C22—124no—
549C22—121no—
550C22—121no—
551C22—122no—
552C22—242no—
553C22—241no—
554C22—241no—
555C22#6387911yescharacteristic
556C22#6392211yescharacteristic
557C22#6397011yescharacteristic
558C4—42no—
559C4—62no—
560C4—122no—
561C4—361no—
562C4—361no—
563C4#6388511yescharacteristic
564C4#6389111yescharacteristic
565C4#6390211yescharacteristic
566C4D3×(C2×D3)⋊C411yescharacteristic
567C3—21no—
568C3#6966311yescharacteristic, complemented
569C3#7036611yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—122no—
573C2—242no—
574C2#1059039511yescharacteristic
575C2#1059040011yescharacteristic
576C2#1059136311yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×#63823C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1883
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10594986C2semidirect
3. C3×#4939C2semidirect
4. C2×C3×#805C2semidirect
5. #10591086C2semidirect
6. #10589389C2semidirect
7. #10589167C2semidirect
25. #63823C4semidirect
38. #4939D3semidirect
39. C2×#805D3semidirect
59. C2×C3×D12C2×C4semidirect
71. #3748C2×C4semidirect
156. C3×D12C22⋊C4semidirect
160. C3×Dic6C22⋊C4semidirect
206. C2×D12C4×D3semidirect
376. D12(C2×D3)⋊C4semidirect
381. Dic6(C2×D3)⋊C4semidirect
489. C32#1883semidirect
568. C3#69663semidirect
569. C3#70366semidirect

Maximal subgroups

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

subgroupindex
#105949862
C2×#638232
C3×#49392
C2×C3×#8052
#105910862
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