Finite Group Databasebeta

← #11793171

Subgroups — #11793171

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63909C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic, complemented
3C3×#4987C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70634—31nomaximal
9#69523—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3722—21no—
20#63909—22no—
21#63909—22no—
22#63636—22no—
23C3×C3⋊#95—21no—
24C3×#807—22no—
25#63564—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×#930—31no—
28C2×#895—31no—
29C2×C3×#107—31no—
30C3×#380—31no—
31C2×#830—31no—
32C2×#821—31no—
33C2×(C2×D3)⋊C8—31no—
34#4987D311yescharacteristic, complemented
35C2×#809—31no—
36C2×#809—31no—
37C2×#809—31no—
38C2×#809—61no—
39C2×#807D311yescharacteristic, complemented
40#4529—31no—
41#4529—31no—
42C23×C3⋊D3—21no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
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)D412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×#626—24no—
62C2×#626—42no—
63C2×#626—42no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77#3722—24no—
78#2033—91noSylow
79C23×C3×C4—31no—
80C22×#67—61no—
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×D12—61no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C22⋊C4—61no—
93#930—62no—
94#930—62no—
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104#895—62no—
105#895—62no—
106C3×#107—62no—
107C3×#95—61no—
108C3⋊#95—21no—
109#830—62no—
110#821—62no—
111(C2×D3)⋊C8—62no—
112#809—62no—
113#809—62no—
114#809—64no—
115#809—62no—
116#807—22no—
117C23×C32C2×D411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—41no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3D812yes—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—41no—
144C4⋊(C3⋊D3)—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158#626—48no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—22no—
161C2×#121—91no—
162C2×#107—31no—
163C2×#102—91no—
164C2×#102—91no—
165C2×C22⋊C8—91no—
166#380—31no—
167#340—91no—
168C24×C3—31no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C23×D3#6711yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—41no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C2×#67—64no—
189C2×#67—122no—
190C2×#67—122no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3#6711yescharacteristic
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—62no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—64no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—121no—
211C2×D12—121no—
212C2×D12—121no—
213C2×D12—122no—
214C2×D12—122no—
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C3×C8—32no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—122no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238C4⋊Dic3—21no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3#6712yes—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8—121no—
253C2×C3⋊C8D1212yescomplemented
254C22×C32#12011yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C22×C32C2×D811yescharacteristic
258C22×C32#13511yescharacteristic
259C22×C32AGL(1,ℤ/8)11yescharacteristic
260C22×C32#13711yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—81no—
265C2×C3⋊D3—81no—
266C2×C3⋊D3—81no—
267C2×C3⋊D3—81no—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—81no—
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12311yescharacteristic
279C32×C4#12411yescharacteristic
280C3×Dic3—41no—
281C3×Dic3—42no—
282C3×Dic3—81no—
283C22×D4—91no—
284C22×D4—181no—
285C23×C4—31no—
286C22×C8—31no—
287C22×C8—91no—
288#121—182no—
289#121—182no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4D3211yescharacteristic
293C2×C22⋊C4—61no—
294C2×C22⋊C4—181no—
295#107—62no—
296#102—182no—
297#102—182no—
298C22⋊C8—182no—
299#95—61no—
300C23×C3—21no—
301C23×C3—32no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—61no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—61no—
308C23×C3D3×D411yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—21no—
313C22×D3—21no—
314C22×D3—21no—
315C22×D3—21no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—122no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C22×D3—121no—
327C22×D3—121no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—121no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—241no—
334C22×D3—241no—
335C22×D3—241no—
336C22×D3—241no—
337C22×D3#21312yes—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4#23511yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4#23911yescharacteristic
376C2×C3×C4#23911yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378#67—128no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388D12—64no—
389D12—62no—
390D12—62no—
391D12—62no—
392D12—62no—
393D12—122no—
394D12—122no—
395D12—122no—
396D12—128no—
397D12—121no—
398D12—121no—
399D12—121no—
400D12—121no—
401C4×D3—41no—
402C4×D3—41no—
403C4×D3—41no—
404C4×D3—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C3⋊C8—122no—
408C3⋊C8—121no—
409C3⋊C8—121no—
410C2×C32#39411yescharacteristic
411C2×C32#44711yescharacteristic
412C2×C32#45211yescharacteristic
413C2×C32#46611yescharacteristic
414C2×C32#46811yescharacteristic
415C2×C32#48011yescharacteristic
416C2×C32#48211yescharacteristic
417C3⋊D3—82no—
418C3×D3—42no—
419C24—31no—
420C24—181no—
421C2×D4—92no—
422C2×D4—184no—
423C2×D4—181no—
424C2×D4—181no—
425C2×D4—181no—
426C2×D4—181no—
427C2×D4—181no—
428C2×D4—362no—
429C2×D4—362no—
430C22×C4—21no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4C2×D3211yescharacteristic
441C2×C8—32no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—181no—
445C2×C8—181no—
446C2×C8—181no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—32no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C22⋊C4—122no—
454C22⋊C4—184no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—121no—
466C22×C3—121no—
467C22×C3—121no—
468C22×C3—121no—
469C22×C3#89411yescharacteristic
470C22×C3#89511yescharacteristic
471C22×C3D3×D811yescharacteristic
472C22×C3#91111yescharacteristic
473C22×C3#91811yescharacteristic
474C22×C3#91911yescharacteristic
475C22×C3#92911yescharacteristic
476C22×C3C2×#21311yescharacteristic
477C22×C3#93711yescharacteristic
478C22×C3#93711yescharacteristic
479C22×C3#93911yescharacteristic
480C22×C3#94211yescharacteristic
481C22×C3#94911yescharacteristic
482C22×C3#95011yescharacteristic
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—41no—
487C2×D3—41no—
488C2×D3—41no—
489C2×D3—41no—
490C2×D3—124no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—242no—
498C2×D3—242no—
499C2×D3—242no—
500C2×D3—242no—
501C2×D3—242no—
502C2×D3—242no—
503C2×D3—241no—
504C2×D3—241no—
505C2×D3—241no—
506C2×D3—241no—
507C2×D3—241no—
508C2×D3—241no—
509C2×D3—241no—
510C2×D3—241no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—82no—
516C3×C4—81no—
517C3×C4—81no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4—241no—
521C3×C4#88311yescharacteristic
522C3×C4#88411yescharacteristic
523C3×C4#88411yescharacteristic
524C3×C4#88511yescharacteristic
525C3×C4#89411yescharacteristic
526C3×C4#89511yescharacteristic
527C3×C4#93011yescharacteristic
528C3×C4#94711yescharacteristic
529Dic3—42no—
530Dic3—41no—
531Dic3—81no—
532C32#203311yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23—182no—
541C23—361no—
542C23—361no—
543C23—361no—
544C23—361no—
545C23—361no—
546C23—361no—
547C23D3×#6711yescharacteristic
548D4—182no—
549D4—182no—
550D4—368no—
551D4—361no—
552D4—361no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4#379611yescharacteristic
570C2×C4#379811yescharacteristic
571C2×C4#379911yescharacteristic
572C2×C4D3×D1211yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4#381111yescharacteristic
575C8—62no—
576C8—361no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—122no—
585C2×C3#488211yescharacteristic
586C2×C3#488311yescharacteristic
587C2×C3#488511yescharacteristic
588C2×C3#488611yescharacteristic
589C2×C3#495911yescharacteristic
590C2×C3#496711yescharacteristic
591C2×C3#499111yescharacteristic
592C2×C3#500311yescharacteristic
593C2×C3#503611yescharacteristic
594C2×C3#503811yescharacteristic
595C2×C3#504711yescharacteristic
596C2×C3#504911yescharacteristic
597C2×C3#515611yescharacteristic
598C2×C3#518711yescharacteristic
599D3—42no—
600D3—244no—
601D3—242no—
602D3—242no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—121no—
607C22—121no—
608C22—121no—
609C22—121no—
610C22—362no—
611C22—362no—
612C22—362no—
613C22—721no—
614C22—721no—
615C22—721no—
616C22—721no—
617C22#6385011yescharacteristic
618C22#6388611yescharacteristic
619C22D3×#21311yescharacteristic
620C22#6392511yescharacteristic
621C22#6394811yescharacteristic
622C22#6394911yescharacteristic
623C22#6398311yescharacteristic
624C4—81no—
625C4—122no—
626C4—121no—
627C4—241no—
628C4#6385311yescharacteristic
629C4#6390611yescharacteristic
630C4#6390711yescharacteristic
631C4#6391011yescharacteristic
632C3—21no—
633C3#6952311yescharacteristic, complemented
634C3#7063411yescharacteristic, complemented
635C2—122no—
636C2—722no—
637C2#1059042211yescharacteristic
638C2#1059042411yescharacteristic
639C2#1059057611yescharacteristic
640C2#1059058511yescharacteristic
641C2#1059129111yescharacteristic
642C2#1059151511yescharacteristic
643C2#1059165711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2033
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
2. C2×#63636C2semidirect
3. C3×#4987C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63564C2semidirect
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
7. #10589163C2semidirect
34. #4987D3semidirect
39. C2×#807D3semidirect
76. C2×C3×C3⋊C8D4semidirect
253. C2×C3⋊C8D12semidirect
532. C32#2033semidirect
633. C3#69523semidirect
634. C3#70634semidirect

Maximal subgroups

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

subgroupindex
C2×#639092
C2×#636362
C3×#49872
C2×C3×#8072
C2×#635642
C2×(C2×D3)⋊(C3⋊C8)2
#105891632
#706343
#695233