Finite Group Databasebeta

← #11792021

Subgroups — #11792021

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#70273—31nomaximal
9#68888—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)—21no—
16#64106—22no—
17#64106—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×#3722—21no—
23#63871—22no—
24#63871—22no—
25C2×#3719—22no—
26C2×#3719—22no—
27C2×#3719—22no—
28C3×#810—22no—
29#63567—22no—
30#63557—22no—
31C2×#946—31no—
32C22×#216—31no—
33C22×Dic12—31no—
34C2×#897—31no—
35C2×#897—31no—
36C2×#897—31no—
37C2×#897—61no—
38C2×C3×#103—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—31no—
41C2×#816—31no—
42C2×#810—31no—
43C2×#810D311yescharacteristic, complemented
44C3×#340—31no—
45#4529D311yescharacteristic, complemented
46C23×C3⋊D3D411yescharacteristic
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3—21no—
56C2×C4×C3⋊D3—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634—21no—
62C2×#634D412yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4D412yes—
73#3752—24no—
74C4⋊(C3⋊Dic3)—24no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3D412yes—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8D412yes—
83Dic3⋊Dic3—24no—
84#3722—24no—
85#3719—28no—
86#2001—91noSylow
87C22×C3×Q8—31no—
88C22×C4×D3—31no—
89C22×C4×D3—31no—
90C22×C4×D3—61no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D311yescharacteristic
101#946—62no—
102#946—62no—
103C2×#216—62no—
104C2×#216—62no—
105C2×#216—62no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—62no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3—62no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—61no—
117C22×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C2×Dic12—62no—
120C2×Dic12—62no—
121C2×Dic12—62no—
122#897—62no—
123#897—62no—
124#897—64no—
125#897—64no—
126#897—62no—
127#897—62no—
128#897—62no—
129#897—62no—
130C3×#103—62no—
131(C2×D3)⋊C8—62no—
132(C2×D3)⋊C8—62no—
133#816—62no—
134#810—22no—
135#810—62no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—21no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3—21no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3Q1612yescomplemented
144C2×C32×C4—22no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159C4×C3⋊D3—41no—
160C4×C3⋊D3—41no—
161C4×C3⋊D3—41no—
162C4×C3⋊D3—41no—
163#634—22no—
164#634—22no—
165#634—41no—
166#634—41no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—41no—
176C3×Dic6—41no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—41no—
179C22×Q16—91no—
180C2×C22⋊Q8—91no—
181C2×C22⋊Q8—91no—
182C2×#103—31no—
183C2×#103—91no—
184C2×C22⋊C8—91no—
185#340—31no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C2×C3×Q8—32no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8—61no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—61no—
208C22×Dic3—62no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
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—121no—
226C2×C4×D3—121no—
227C2×C4×D3—121no—
228C2×C4×D3—121no—
229C2×Dic6—21no—
230C2×Dic6—21no—
231C2×Dic6—21no—
232C2×Dic6—21no—
233C2×Dic6—21no—
234C2×Dic6—32no—
235C2×Dic6—32no—
236C2×Dic6—62no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—62no—
246C2×Dic6—61no—
247C2×Dic6—61no—
248C2×Dic6—121no—
249C2×Dic6—121no—
250C2×Dic6—121no—
251C2×Dic6—121no—
252C2×Dic6D1212yes—
253C2×C3×C8—32no—
254C2×C3×C8—61no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8—61no—
258C2×C3×C8—61no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4D1212yes—
266C3×C4⋊C4#6712yes—
267#216—68no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—68no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—21no—
274C4⋊Dic3—64no—
275C4⋊Dic3—68no—
276C4⋊Dic3—64no—
277C4⋊Dic3—64no—
278C4⋊Dic3D1212yes—
279Dic3⋊C4—64no—
280C2×C3⋊C8—21no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8D1212yes—
286Dic12—68no—
287C22×C32#12011yescharacteristic
288C22×C32#12011yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32C2×Q1611yescharacteristic
291C22×C32#13511yescharacteristic
292C22×C32#13711yescharacteristic
293C22×C32#13711yescharacteristic
294C2×C3⋊D3—22no—
295C2×C3⋊D3—22no—
296C2×C3⋊D3—22no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3⋊D3—41no—
301C32×C4—42no—
302C32×C4#12011yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4#12111yescharacteristic
305C32×C4#12711yescharacteristic
306C3⋊Dic3—42no—
307C3⋊Dic3—41no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×Q8—31no—
311C22×Q8—91no—
312C23×C4—91no—
313C2×Q16—182no—
314C2×Q16—182no—
315C2×Q16—182no—
316C22×C8—31no—
317C22×C8—31no—
318C22⋊Q8—182no—
319C22⋊Q8—182no—
320C22⋊Q8—182no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—181no—
324C2×C4⋊C4—181no—
325C2×C4⋊C4D3211yescharacteristic
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#103—62no—
329#103—182no—
330C22⋊C8—182no—
331C23×C3—21no—
332C23×C3D3×D411yescharacteristic
333C23×C3D3×D411yescharacteristic
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C3×Q8—62no—
356C3×Q8—62no—
357C3×Q8—121no—
358C3×Q8—121no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4C2×D1211yescharacteristic
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4C2×D1211yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4#23911yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—62no—
399C2×Dic3—64no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C4×D3—122no—
417C4×D3—122no—
418C4×D3—122no—
419C4×D3—122no—
420C4×D3—121no—
421C4×D3—121no—
422C4×D3—121no—
423C4×D3—121no—
424C4×D3—121no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—121no—
428Dic6—22no—
429Dic6—22no—
430Dic6—41no—
431Dic6—41no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—122no—
437Dic6—122no—
438Dic6—122no—
439Dic6—122no—
440Dic6—121no—
441Dic6—121no—
442Dic6—121no—
443Dic6—121no—
444C3×C8—62no—
445C3×C8—121no—
446C3⋊C8—22no—
447C3⋊C8—41no—
448C2×C32#39211yescharacteristic
449C2×C32#45111yescharacteristic
450C2×C32#45111yescharacteristic
451C2×C32#45211yescharacteristic
452C2×C32#45211yescharacteristic
453C2×C32#46711yescharacteristic
454C2×C32#47011yescharacteristic
455C3⋊D3—42no—
456C24—91no—
457C2×Q8—32no—
458C2×Q8—61no—
459C2×Q8—61no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×Q8—61no—
463C2×Q8—92no—
464C2×Q8—181no—
465C2×Q8—181no—
466C2×Q8—181no—
467C2×Q8—181no—
468C2×Q8—181no—
469C22×C4—21no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—91no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481Q16—188no—
482C2×C8—32no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—61no—
488C4⋊C4—21no—
489C4⋊C4—32no—
490C4⋊C4—61no—
491C4⋊C4—184no—
492C4⋊C4—184no—
493C4⋊C4#62612yes—
494C22⋊C4—184no—
495C22⋊C4—184no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3#88211yescharacteristic
504C22×C3#88211yescharacteristic
505C22×C3#88211yescharacteristic
506C22×C3#88411yescharacteristic
507C22×C3#89511yescharacteristic
508C22×C3#91211yescharacteristic
509C22×C3#91511yescharacteristic
510C22×C3#91511yescharacteristic
511C22×C3#91511yescharacteristic
512C22×C3#91611yescharacteristic
513C22×C3D3×Q1611yescharacteristic
514C22×C3D3×Q1611yescharacteristic
515C22×C3#91811yescharacteristic
516C22×C3#93711yescharacteristic
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—44no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—122no—
546C3×C4—122no—
547C3×C4#87411yescharacteristic
548C3×C4#88211yescharacteristic
549C3×C4#88211yescharacteristic
550C3×C4#88411yescharacteristic
551C3×C4#89511yescharacteristic
552C3×C4#89511yescharacteristic
553C3×C4#93011yescharacteristic
554C3×C4#94011yescharacteristic
555Dic3—42no—
556Dic3—42no—
557Dic3—124no—
558Dic3—122no—
559Dic3—122no—
560Dic3—121no—
561Dic3—122no—
562Dic3—121no—
563C32#200111yescharacteristic, complemented, Sylow
564C23—92no—
565C23—181no—
566C23—181no—
567C23—181no—
568C23—181no—
569C23—181no—
570C23—181no—
571C23#381111yescharacteristic
572Q8—62no—
573Q8—62no—
574Q8—121no—
575Q8—121no—
576Q8—182no—
577Q8—182no—
578Q8—361no—
579Q8—361no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—121no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—121no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—182no—
592C2×C4—181no—
593C2×C4—361no—
594C2×C4—361no—
595C2×C4—361no—
596C2×C4—361no—
597C2×C4—361no—
598C2×C4—361no—
599C2×C4#379911yescharacteristic
600C2×C4D3×D1211yescharacteristic
601C2×C4D3×D1211yescharacteristic
602C2×C4D3×D1211yescharacteristic
603C2×C4C2×#62611yescharacteristic
604C2×C4#381111yescharacteristic
605C8—62no—
606C8—121no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3#467111yescharacteristic
615C2×C3#478311yescharacteristic
616C2×C3#478311yescharacteristic
617C2×C3#480811yescharacteristic
618C2×C3#480911yescharacteristic
619C2×C3#480911yescharacteristic
620C2×C3#480911yescharacteristic
621C2×C3#481311yescharacteristic
622C2×C3#481611yescharacteristic
623C2×C3#486711yescharacteristic
624C2×C3#488711yescharacteristic
625C2×C3#496011yescharacteristic
626C2×C3#517311yescharacteristic
627C2×C3#518611yescharacteristic
628D3—124no—
629D3—122no—
630D3—122no—
631C22—182no—
632C22—182no—
633C22—182no—
634C22—361no—
635C22—361no—
636C22—361no—
637C22—361no—
638C22#6391011yescharacteristic
639C22#6392311yescharacteristic
640C22#6393111yescharacteristic
641C22#6393611yescharacteristic
642C22#6394411yescharacteristic
643C22#6395111yescharacteristic
644C22#6398111yescharacteristic
645C4—42no—
646C4—122no—
647C4—122no—
648C4—361no—
649C4—362no—
650C4#6390911yescharacteristic
651C4#6391011yescharacteristic
652C4#6391111yescharacteristic
653C4#6392311yescharacteristic
654C3—21no—
655C3#6888811yescharacteristic, complemented
656C3#7027311yescharacteristic, complemented
657C2—362no—
658C2#1059052411yescharacteristic
659C2#1059052511yescharacteristic
660C2#1059060511yescharacteristic
661C2#1059061811yescharacteristic
662C2#1059139511yescharacteristic
663C2#1059146611yescharacteristic
664C2#1059160311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2001
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. C22×#3719C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63567C2semidirect
7. C3×#4529C2semidirect
43. C2×#810D3semidirect
45. #4529D3semidirect
143. C22×C3⋊D3Q16semidirect
563. C32#2001semidirect
655. C3#68888semidirect
656. C3#70273semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#638712
C22×#37192
C2×C3×#8102
C2×#635672
C2×#635572
C3×#45292
#702733
#688883