Finite Group Databasebeta

← #11794068

Subgroups — #11794068

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3717C211yesmaximal, characteristic
2#10592687C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#70280—31nomaximal
9#68863—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3717—22no—
20C2×#3717—22no—
21C2×#3717—22no—
22C3×#810—22no—
23#63579—21no—
24#63579—21no—
25#63572—22no—
26#63564—22no—
27C22×#215—31no—
28C22×#204—31no—
29C2×C3×#103—31no—
30#5229—31no—
31C2×#821—31no—
32C2×Dic3⋊C8—31no—
33C2×Dic3⋊C8—31no—
34#4988—31no—
35#4988—31no—
36#4988—61no—
37#4973—31no—
38C2×#810D311yescharacteristic, complemented
39C2×#809—31no—
40C3×#340—31no—
41#4529D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63#3752—42no—
64#3752—42no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#3717—28no—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×D12—31no—
79C22×D12—31no—
80C22×D12—61no—
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×#215—62no—
89C2×#215—62no—
90C2×#215—62no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—62no—
96C2×(C2×D3)⋊C4—62no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C22×C3⋊C8C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103C2×#204—62no—
104C2×#204—62no—
105C2×#204—62no—
106C3×#103—62no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#821—62no—
112Dic3⋊C8—62no—
113Dic3⋊C8—62no—
114#810—22no—
115#809—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—22no—
118C22×C3⋊D3—41no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3SD1612yescomplemented
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—41no—
155C22×SD16—91no—
156C2×C4⋊C8—91no—
157C2×#103—31no—
158C2×#102—91no—
159#391—91no—
160#390—91no—
161#340—31no—
162C23×D3—62no—
163C23×D3—61no—
164C23×D3—61no—
165C2×C3×Q8—32no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C22×C3×C4—22no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—121no—
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×Dic6#6712yes—
211C2×C3×C8—32no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225#215—68no—
226(C2×D3)⋊C4—122no—
227(C2×D3)⋊C4—122no—
228(C2×D3)⋊C4—124no—
229(C2×D3)⋊C4—124no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—121no—
239C4×Dic3—121no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8D1212yes—
246#204—68no—
247C22×C32#12111yescharacteristic
248C22×C32#12111yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32C2×SD1611yescharacteristic
251C22×C32#13511yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C22×C32#13711yescharacteristic
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—81no—
258C2×C3⋊D3—81no—
259C2×C3⋊D3—81no—
260C2×C3⋊D3—81no—
261C32×C4—81no—
262C32×C4#12011yescharacteristic
263C32×C4#12311yescharacteristic
264C32×C4#12311yescharacteristic
265C32×C4#12411yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3—41no—
268C3×Dic3—42no—
269C3×Dic3—81no—
270C22×Q8—31no—
271C22×D4—91no—
272C2×SD16—182no—
273C2×SD16—182no—
274C2×SD16—182no—
275C22×C8—31no—
276C22×C8—31no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4D3211yescharacteristic
279C2×C22⋊C4—181no—
280C2×C22⋊C4—181no—
281C2×C42—91no—
282C4⋊C8—182no—
283#103—62no—
284#102—182no—
285#95—181no—
286#95—181no—
287C23×C3—21no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—122no—
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—121no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—121no—
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—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—62no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23911yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—32no—
350C2×Dic3—32no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—62no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—122no—
378D12—122no—
379D12—122no—
380D12—121no—
381D12—121no—
382D12—121no—
383D12—121no—
384Dic6—22no—
385Dic6—22no—
386Dic6—41no—
387Dic6—41no—
388C3×C8—62no—
389C3×C8—121no—
390C3⋊C8—22no—
391C3⋊C8—41no—
392C2×C32#39411yescharacteristic
393C2×C32#46011yescharacteristic
394C2×C32#46111yescharacteristic
395C2×C32#46311yescharacteristic
396C2×C32#46411yescharacteristic
397C2×C32#46511yescharacteristic
398C2×C32#46811yescharacteristic
399C3⋊D3—82no—
400C24—181no—
401C2×Q8—32no—
402C2×Q8—61no—
403C2×Q8—61no—
404C2×Q8—61no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×D4—92no—
408C2×D4—181no—
409C2×D4—181no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C22×C4—21no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4C2×D3211yescharacteristic
419SD16—188no—
420C2×C8—32no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—61no—
425C2×C8—61no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C22⋊C4—362no—
431C22⋊C4—362no—
432C42—181no—
433C42—181no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3#88411yescharacteristic
442C22×C3#88411yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3#88411yescharacteristic
445C22×C3#89511yescharacteristic
446C22×C3#91111yescharacteristic
447C22×C3D3×SD1611yescharacteristic
448C22×C3D3×SD1611yescharacteristic
449C22×C3#91411yescharacteristic
450C22×C3#91611yescharacteristic
451C22×C3#91811yescharacteristic
452C22×C3#91811yescharacteristic
453C22×C3#91911yescharacteristic
454C22×C3#93911yescharacteristic
455C2×D3—124no—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—242no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—241no—
469C2×D3—241no—
470C2×D3—241no—
471C2×D3—241no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—241no—
475C2×D3—241no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—82no—
481C3×C4—81no—
482C3×C4—81no—
483C3×C4—122no—
484C3×C4—241no—
485C3×C4#87511yescharacteristic
486C3×C4#88211yescharacteristic
487C3×C4#88311yescharacteristic
488C3×C4#88511yescharacteristic
489C3×C4#89411yescharacteristic
490C3×C4#89411yescharacteristic
491C3×C4#92911yescharacteristic
492C3×C4#93711yescharacteristic
493Dic3—42no—
494Dic3—62no—
495Dic3—62no—
496Dic3—81no—
497Dic3—122no—
498Dic3—122no—
499Dic3—121no—
500Dic3—121no—
501C32#205511yescharacteristic, complemented, Sylow
502C23—182no—
503C23—361no—
504C23—361no—
505C23—361no—
506C23—361no—
507C23—361no—
508C23—361no—
509C23#381111yescharacteristic
510Q8—62no—
511Q8—62no—
512Q8—121no—
513Q8—121no—
514D4—182no—
515D4—182no—
516D4—361no—
517D4—361no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—62no—
522C2×C4—92no—
523C2×C4—121no—
524C2×C4—121no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4#379811yescharacteristic
534C2×C4#379911yescharacteristic
535C2×C4D3×D1211yescharacteristic
536C2×C4#380211yescharacteristic
537C2×C4#380411yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C8—62no—
540C8—121no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3#467211yescharacteristic
549C2×C3#476211yescharacteristic
550C2×C3#478711yescharacteristic
551C2×C3#479811yescharacteristic
552C2×C3#480711yescharacteristic
553C2×C3#481211yescharacteristic
554C2×C3#481811yescharacteristic
555C2×C3#481811yescharacteristic
556C2×C3#481911yescharacteristic
557C2×C3#486411yescharacteristic
558C2×C3#488611yescharacteristic
559C2×C3#495911yescharacteristic
560C2×C3#516311yescharacteristic
561C2×C3#518511yescharacteristic
562D3—244no—
563D3—242no—
564D3—242no—
565C22—362no—
566C22—362no—
567C22—362no—
568C22—721no—
569C22—721no—
570C22—721no—
571C22—721no—
572C22#6391011yescharacteristic
573C22#6391211yescharacteristic
574C22#6393011yescharacteristic
575C22#6393711yescharacteristic
576C22#6394511yescharacteristic
577C22#6395011yescharacteristic
578C22#6397111yescharacteristic
579C4—81no—
580C4—122no—
581C4—182no—
582C4—241no—
583C4—361no—
584C4#6385011yescharacteristic
585C4#6385211yescharacteristic
586C4#6385411yescharacteristic
587C4#6392211yescharacteristic
588C3—21no—
589C3#6886311yescharacteristic, complemented
590C3#7028011yescharacteristic, complemented
591C2—722no—
592C2#1059052211yescharacteristic
593C2#1059052311yescharacteristic
594C2#1059054011yescharacteristic
595C2#1059056511yescharacteristic
596C2#1059129211yescharacteristic
597C2#1059144411yescharacteristic
598C2#1059157911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#810C2semidirect
4. #10591221C2semidirect
5. C2×#63572C2semidirect
7. C3×#4529C2semidirect
38. C2×#810D3semidirect
41. #4529D3semidirect
138. C2×C3⋊Dic3SD16semidirect
501. C32#2055semidirect
589. C3#68863semidirect
590. C3#70280semidirect

Maximal subgroups

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

subgroupindex
C22×#37172
#105926872
C2×C3×#8102
#105912212
C2×#635722
C2×#635642
C3×#45292
#702803
#688633