Finite Group Databasebeta

← #11793174

Subgroups — #11793174

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×C3×#807C211yesmaximal, characteristic, complemented
3#10591325C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8#70634—31nomaximal
9#68822—31nomaximal
10C22×C4⋊(C3⋊D3)—21no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15#64104—22no—
16#64104—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C3×#807—22no—
23#63579—21no—
24#63564—22no—
25#63564—22no—
26#63557—22no—
27C2×#895—31no—
28C2×#895—31no—
29C2×#895—61no—
30C2×C3×#107—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×(C2×D3)⋊C8—31no—
34C2×(C2×D3)⋊C8—31no—
35#4987—31no—
36#4987—31no—
37C2×#809—31no—
38C2×#809—31no—
39C2×#807D311yescharacteristic, complemented
40C3×#340—31no—
41#4529D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C23×C3⋊D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
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)—24no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—42no—
54C2×C4⋊(C3⋊D3)—42no—
55C2×C4⋊(C3⋊D3)D412yes—
56C2×C4×C3⋊D3—21no—
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4D412yes—
66#3752—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77#3722—42no—
78#2033—91noSylow
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×D12—61no—
83C22×D12—61no—
84C22×D12—62no—
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—62no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104#895—62no—
105#895—62no—
106#895—64no—
107#895—64no—
108#895—62no—
109#895—62no—
110C3×#107—62no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#821—62no—
114#821—62no—
115(C2×D3)⋊C8—62no—
116(C2×D3)⋊C8—62no—
117#809—62no—
118#809—62no—
119#807—22no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3D812yes—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—48no—
150C4⋊(C3⋊D3)—41no—
151C4⋊(C3⋊D3)—41no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154C4×C3⋊D3—41no—
155C4×C3⋊D3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C3×C3⋊C8—22no—
163C3×C3⋊C8—41no—
164C2×#121—91no—
165C2×#107—31no—
166C2×#102—91no—
167C2×#102—91no—
168C2×C22⋊C8—91no—
169#380—91no—
170#340—31no—
171C23×D3—31no—
172C23×D3—31no—
173C23×D3—61no—
174C23×D3—62no—
175C23×D3—61no—
176C23×D3—61no—
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—61no—
190C2×D12—32no—
191C2×D12—32no—
192C2×D12—62no—
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—68no—
202C2×D12—64no—
203C2×D12—64no—
204C2×D12—62no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—121no—
208C2×D12—121no—
209C2×D12—121no—
210C2×D12—121no—
211C2×D12—122no—
212C2×D12—122no—
213C2×D12—124no—
214C2×D12—124no—
215C2×D12—122no—
216C2×D12—122no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—121no—
232C2×C4×D3—121no—
233C2×C4×D3—121no—
234C2×C4×D3—121no—
235C2×C3×C8—32no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C2×C3×C8—61no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4D1212yes—
250C3×C4⋊C4#6712yes—
251(C2×D3)⋊C4—68no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8D1212yescomplemented
266C22×C32#12011yescharacteristic
267C22×C32#12111yescharacteristic
268C22×C32#12311yescharacteristic
269C22×C32C2×D811yescharacteristic
270C22×C32#13511yescharacteristic
271C22×C32AGL(1,ℤ/8)11yescharacteristic
272C22×C32#13711yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—81no—
284C2×C3⋊D3—81no—
285C2×C3⋊D3—81no—
286C2×C3⋊D3—81no—
287C32×C4—42no—
288C32×C4#12111yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12311yescharacteristic
291C32×C4#12411yescharacteristic
292C3⋊Dic3—41no—
293C3×Dic3—81no—
294C3×Dic3—81no—
295C22×D4—91no—
296C22×D4—181no—
297C23×C4—91no—
298C22×C8—31no—
299C22×C8—31no—
300#121—182no—
301#121—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C4⋊C4D3211yescharacteristic
305C2×C22⋊C4—181no—
306C2×C22⋊C4—181no—
307#107—62no—
308#102—182no—
309#102—182no—
310C22⋊C8—182no—
311#95—181no—
312C23×C3—21no—
313C23×C3D3×D411yescharacteristic
314C23×C3D3×D411yescharacteristic
315C22×D3—32no—
316C22×D3—32no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—61no—
321C22×D3—61no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—64no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—122no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3—121no—
356C22×D3—121no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4#23511yescharacteristic
382C2×C3×C4#23511yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4#23911yescharacteristic
387C2×C3×C4#23911yescharacteristic
388C2×C3×C4#23911yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—41no—
393C2×Dic3—41no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—122no—
410D12—122no—
411D12—122no—
412D12—122no—
413D12—1216no—
414D12—128no—
415D12—128no—
416D12—121no—
417D12—121no—
418D12—121no—
419D12—121no—
420C4×D3—122no—
421C4×D3—122no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—121no—
428C4×D3—121no—
429C4×D3—121no—
430C4×D3—121no—
431C4×D3—121no—
432C3×C8—62no—
433C3×C8—121no—
434C3⋊C8—22no—
435C3⋊C8—41no—
436C2×C32#39411yescharacteristic
437C2×C32#44711yescharacteristic
438C2×C32#45211yescharacteristic
439C2×C32#46611yescharacteristic
440C2×C32#46811yescharacteristic
441C2×C32#48011yescharacteristic
442C2×C32#48211yescharacteristic
443C3⋊D3—42no—
444C3⋊D3—82no—
445C24—91no—
446C24—181no—
447C2×D4—92no—
448C2×D4—184no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—362no—
455C2×D4—362no—
456C22×C4—21no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—91no—
460C22×C4—181no—
461C22×C4—181no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4C2×D3211yescharacteristic
467C2×C8—32no—
468C2×C8—61no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8—61no—
473C4⋊C4—21no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C4⋊C4—61no—
478C4⋊C4#62612yes—
479C22⋊C4—184no—
480C22⋊C4—362no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3#88211yescharacteristic
489C22×C3#88411yescharacteristic
490C22×C3#89411yescharacteristic
491C22×C3#89411yescharacteristic
492C22×C3#89511yescharacteristic
493C22×C3D3×D811yescharacteristic
494C22×C3D3×D811yescharacteristic
495C22×C3#91111yescharacteristic
496C22×C3#91411yescharacteristic
497C22×C3#91611yescharacteristic
498C22×C3#91811yescharacteristic
499C22×C3#91811yescharacteristic
500C22×C3#91911yescharacteristic
501C22×C3#93711yescharacteristic
502C2×D3—64no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—124no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—242no—
536C2×D3—241no—
537C2×D3—241no—
538C2×D3—241no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3—241no—
542C2×D3—241no—
543C2×D3—241no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—44no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—241no—
552C3×C4—241no—
553C3×C4#87511yescharacteristic
554C3×C4#88411yescharacteristic
555C3×C4#89411yescharacteristic
556C3×C4#89411yescharacteristic
557C3×C4#89511yescharacteristic
558C3×C4#89511yescharacteristic
559C3×C4#93011yescharacteristic
560C3×C4#94711yescharacteristic
561Dic3—81no—
562Dic3—81no—
563Dic3—122no—
564Dic3—121no—
565Dic3—121no—
566C32#203311yescharacteristic, complemented, Sylow
567C23—92no—
568C23—181no—
569C23—181no—
570C23—181no—
571C23—181no—
572C23—181no—
573C23—181no—
574C23—182no—
575C23—361no—
576C23—361no—
577C23—361no—
578C23—361no—
579C23—361no—
580C23—361no—
581C23#381111yescharacteristic
582D4—182no—
583D4—182no—
584D4—368no—
585D4—361no—
586D4—361no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—121no—
591C2×C4—121no—
592C2×C4—121no—
593C2×C4—121no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—181no—
599C2×C4—361no—
600C2×C4—361no—
601C2×C4—361no—
602C2×C4—361no—
603C2×C4#379911yescharacteristic
604C2×C4#379911yescharacteristic
605C2×C4#379911yescharacteristic
606C2×C4D3×D1211yescharacteristic
607C2×C4C2×#62611yescharacteristic
608C2×C4#381111yescharacteristic
609C8—62no—
610C8—121no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3#467211yescharacteristic
619C2×C3#477311yescharacteristic
620C2×C3#477511yescharacteristic
621C2×C3#480811yescharacteristic
622C2×C3#481211yescharacteristic
623C2×C3#486611yescharacteristic
624C2×C3#488211yescharacteristic
625C2×C3#488211yescharacteristic
626C2×C3#488311yescharacteristic
627C2×C3#488511yescharacteristic
628C2×C3#488611yescharacteristic
629C2×C3#499111yescharacteristic
630C2×C3#515611yescharacteristic
631C2×C3#518711yescharacteristic
632D3—124no—
633D3—122no—
634D3—122no—
635D3—244no—
636D3—242no—
637D3—242no—
638C22—182no—
639C22—182no—
640C22—182no—
641C22—361no—
642C22—361no—
643C22—361no—
644C22—361no—
645C22—362no—
646C22—362no—
647C22—362no—
648C22—721no—
649C22—721no—
650C22—721no—
651C22—721no—
652C22#6389711yescharacteristic
653C22#6391011yescharacteristic
654C22#6392611yescharacteristic
655C22#6393711yescharacteristic
656C22#6394511yescharacteristic
657C22#6395011yescharacteristic
658C22#6398111yescharacteristic
659C4—42no—
660C4—241no—
661C4—241no—
662C4—361no—
663C4#6386411yescharacteristic
664C4#6389711yescharacteristic
665C4#6390911yescharacteristic
666C4#6391011yescharacteristic
667C3—21no—
668C3#6882211yescharacteristic, complemented
669C3#7063411yescharacteristic, complemented
670C2—362no—
671C2—722no—
672C2#1059044211yescharacteristic
673C2#1059045111yescharacteristic
674C2#1059050911yescharacteristic
675C2#1059052211yescharacteristic
676C2#1059132111yescharacteristic
677C2#1059145611yescharacteristic
678C2#1059160211yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#64104C2
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×C3×#807C2semidirect
3. #10591325C2semidirect
4. C2×#63564C2semidirect
5. C2×#63564C2semidirect
6. C2×#63557C2semidirect
7. C3×#4529C2semidirect
39. C2×#807D3semidirect
41. #4529D3semidirect
76. C2×C3×C3⋊C8D4semidirect
265. C2×C3⋊C8D12semidirect
566. C32#2033semidirect
668. C3#68822semidirect
669. C3#70634semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8072
#105913252
C2×#635642
C2×#635572
C3×#45292
#706343
#688223