Finite Group Databasebeta

← C2×#13072217 #14921794

Subgroups — C2×#13072217 #14921794

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic
3C22×Q8×Dic11C211yesmaximal, characteristic, complemented
4#13072217C2116yesmaximal, direct product factor
5C2×#10622597C212yesmaximal, complemented
6C2×#10622561C212yesmaximal
7C2×#10622587C211yesmaximal, characteristic, complemented
8C2×#10622586C211yesmaximal, characteristic, complemented
9C2×#10622585C212yesmaximal, complemented
10C2×#10622558C212yesmaximal
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic
12C22×C11×C22⋊Q8C211yesmaximal, characteristic
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×Dic22C2211yescharacteristic
16C2×C11×C22⋊Q8—28no—
17C2×C11×C22⋊Q8C2218yes—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C2×Q8×Dic11—28no—
25C2×Q8×Dic11C2218yescomplemented
26C2×#66997—28no—
27C2×#66997C2218yescomplemented
28C22×C4⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C2×#66977—28no—
31C2×#66977C2218yes—
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2212yes—
34C22×Dic11⋊C4C2212yes—
35C22×Dic11⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2212yes—
39C4×C22⋊Dic11C2218yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622597C22116yescomplemented
46#10622587C2218yescomplemented
47#10622586C2218yescomplemented
48#10622585C22116yescomplemented
49#10622561C22116yes—
50#10622558C22116yes—
51C25×C11C2311yescharacteristic
52C22×Q8×C11—24no—
53C22×Q8×C11—24no—
54C22×Q8×C11D418yes—
55C22×Q8×C11C2314yes—
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11—24no—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2314yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C22×Dic22—24no—
71C22×Dic22—24no—
72C22×Dic22—24no—
73C22×Dic22C2314yes—
74C11×C22⋊Q8—232no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—28no—
77C2×C11×C4⋊C4C2318yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11Q818yescomplemented
84C2×C22⋊Dic11C2318yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2314yes—
87Q8×Dic11—232no—
88#66997—232no—
89C2×C4⋊Dic11—28no—
90C2×C4⋊Dic11D418yes—
91C2×C4⋊Dic11C2318yes—
92C2×C4⋊Dic11C2314yes—
93#66977—232no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2318yes—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102C2×C4×Dic11—24no—
103C2×C4×Dic11—24no—
104C2×C4×Dic11—28no—
105C2×C4×Dic11C2318yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C2×#2429—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11C2×Q814yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C2×Q8×C11—232no—
124C2×Q8×C11—28no—
125C2×Q8×C11—28no—
126C2×Q8×C11C2×D4116yes—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—28no—
136C22×C4×C11—28no—
137C22×C4×C11—28no—
138C22×C4×C11—416no—
139C22×C4×C11C2×D418yes—
140C22×C4×C11C2×D414yes—
141C22×C4×C11C2×D414yes—
142C22×C4×C11#4114yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2412yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11C2×D418yes—
162C22×Dic11C2×Q814yes—
163C22×Dic11C2×Q814yes—
164C22×Dic11#4114yes—
165C22×Dic11C2412yes—
166C22×Dic11C2414yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C2×Dic22—28no—
172C2×Dic22—28no—
173C2×Dic22—28no—
174C2×Dic22—416no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—216no—
177C11×C22⋊C4—216no—
178C22⋊Dic11—216no—
179C22⋊Dic11—28no—
180C22⋊Dic11C2×Q8116yescomplemented
181C4⋊Dic11—216no—
182C4⋊Dic11C2×D4116yes—
183Dic11⋊C4—216no—
184Dic11⋊C4—216no—
185Dic11⋊C4—216no—
186Dic11⋊C4—216no—
187C4×Dic11—216no—
188C4×Dic11—28no—
189C4×Dic11—28no—
190C22×C4⋊Q8—111no—
191C22×C22⋊Q8—111no—
192C22×C22⋊Q8D1111yescharacteristic
193C22×C4×Q8—111no—
194#2429—1116no—
195C2×#398—112no—
196C2×#396—112no—
197C2×#391—111no—
198C2×#389—112no—
199C2×#389—111no—
200C2×#388—112no—
201C2×C4×C22⋊C4—111no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—28no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11C22×D412yes—
216C23×C11C22×D412yes—
217C23×C11C22×Q814yes—
218C23×C11C22×Q812yes—
219C23×C11C2×#4112yes—
220C23×C11C2×#4112yes—
221C23×C112−1+412yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224Q8×C11—232no—
225C2×C4×C11—216no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11—48no—
236C2×C4×C11—416no—
237C2×C4×C11#121116yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D418yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C2×#4114yes—
242C2×Dic11—216no—
243C2×Dic11—28no—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—48no—
261C2×Dic11—44no—
262C2×Dic11C22×D418yes—
263C2×Dic11C22×Q814yes—
264C2×Dic11C22×Q814yes—
265C2×Dic11C2×#4114yes—
266Dic22—416no—
267C23×Q8—111no—
268C23×Q8C2×D1111yescharacteristic
269C24×C4C2×D1111yescharacteristic
270C2×C4⋊Q8—118no—
271C2×C4⋊Q8—228no—
272C2×C22⋊Q8—28no—
273C2×C22⋊Q8—118no—
274C2×C22⋊Q8—228no—
275C2×C22⋊Q8C2×D1118yes—
276C2×C4×Q8—118no—
277C2×C4×Q8—228no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4C2×D1112yes—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4—111no—
287C22×C22⋊C4—111no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4C2×D1112yes—
290C22×C42—111no—
291C22×C42—112no—
292C22×C42—111no—
293#398—1116no—
294#396—1116no—
295#391—118no—
296#389—1116no—
297#389—118no—
298#388—1116no—
299C4×C22⋊C4—118no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95—112no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—416no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11C2×#12114yes—
314C22×C11#53314yes—
315C22×C11#54114yes—
316C22×C11#54714yes—
317C22×C11#54814yes—
318C22×C11D4×Q814yes—
319C22×C11D4×Q814yes—
320C22×C11C23×D411yescharacteristic
321C22×C11C23×D411yescharacteristic
322C22×C11C23×Q811yescharacteristic
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C2×2−1+411yescharacteristic
326C22×C11C2×2−1+411yescharacteristic
327C4×C11—28no—
328C4×C11—42no—
329C4×C11—44no—
330C4×C11C2×#12118yes—
331Dic11—28no—
332Dic11—24no—
333Dic11—24no—
334Dic11—24no—
335Dic11—44no—
336Dic11—42no—
337C25C22×D1111yescharacteristic
338C22×Q8—24no—
339C22×Q8—24no—
340C22×Q8—114no—
341C22×Q8—224no—
342C22×Q8—224no—
343C22×Q8—224no—
344C22×Q8C22⋊D1118yes—
345C22×Q8C22×D1114yes—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—112no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—112no—
354C23×C4—111no—
355C23×C4C22×D1114yes—
356C23×C4C22×D1112yes—
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1112yes—
359C23×C4C22×D1111yescharacteristic
360C4⋊Q8—2232no—
361C22⋊Q8—232no—
362C22⋊Q8—2232no—
363C4×Q8—2232no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—118no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—118no—
370C2×C4⋊C4—118no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—228no—
374C2×C4⋊C4—228no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4—228no—
378C2×C4⋊C4C22×D1114yes—
379C2×C4⋊C4C22×D1118yes—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—228no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4C22×D1118yes—
388C2×C42—114no—
389C2×C42—118no—
390C2×C42—114no—
391C2×C42—228no—
392C2×C42—224no—
393C2×C42—224no—
394#95—114no—
395#95—114no—
396#95—118no—
397#95—118no—
398#95—118no—
399C2×C11—44no—
400C2×C11#242918yescomplemented
401C2×C11C22×#12111yescharacteristic
402C2×C11C2×#53311yescharacteristic
403C2×C11C2×#54111yescharacteristic
404C2×C11C2×#54711yescharacteristic
405C2×C11C2×#54811yescharacteristic
406C2×C11C2×D4×Q811yescharacteristic
407C2×C11C2×D4×Q811yescharacteristic
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24Q8×D1114yes—
415C24C23×D1112yes—
416C24C23×D1111yescharacteristic
417C2×Q8—232no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—228no—
421C2×Q8—228no—
422C2×Q8—228no—
423C2×Q8—4416no—
424C2×Q8C2×C22⋊D11116yes—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—416no—
437C22×C4—118no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—114no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—224no—
461C22×C4D4×D1114yes—
462C22×C4#434114yes—
463C22×C4C2×C22⋊D1118yes—
464C22×C4C2×C22⋊D1114yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1114yes—
468C22×C4C23×D1112yes—
469C4⋊C4—28no—
470C4⋊C4—216no—
471C4⋊C4—1116no—
472C4⋊C4—2216no—
473C4⋊C4—2216no—
474C4⋊C4—2216no—
475C4⋊C4—2216no—
476C4⋊C4—2216no—
477C22⋊C4—216no—
478C22⋊C4—1116no—
479C22⋊C4—2216no—
480C22⋊C4—228no—
481C42—2216no—
482C42—228no—
483C42—228no—
484C11C2×#242911yescharacteristic, complemented, Sylow
485C23—28no—
486C23—28no—
487C23—28no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23C2×D4×D1112yes—
499C23C2×#434112yes—
500C23C2×Q8×D1114yes—
501C23C2×Q8×D1112yes—
502C23#6704012yes—
503C23#41×D1112yes—
504C23#6704312yes—
505C23C22×C22⋊D1112yes—
506C23C24×D1111yescharacteristic
507Q8—232no—
508Q8—4416no—
509C2×C4—216no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4—416no—
521C2×C4—118no—
522C2×C4—114no—
523C2×C4—114no—
524C2×C4—114no—
525C2×C4—228no—
526C2×C4—228no—
527C2×C4—2216no—
528C2×C4—228no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—448no—
544C2×C4—444no—
545C2×C4#66992116yes—
546C2×C4C2×D4×D1114yes—
547C2×C4C2×#434114yes—
548C2×C4C22×C22⋊D1118yes—
549C2×C4C22×C22⋊D1114yes—
550C22—24no—
551C22—24no—
552C22—24no—
553C22—416no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22#1062315314yes—
559C22#1062315614yes—
560C22#1062316214yes—
561C22#1062316314yes—
562C22C2×#6699214yes—
563C22Q8×C22⋊D1114yes—
564C22#1062336214yes—
565C22C22×D4×D1111yescharacteristic
566C22C22×#434111yescharacteristic
567C22C22×Q8×D1111yescharacteristic
568C22C2×#6704011yescharacteristic
569C22C2×#41×D1111yescharacteristic
570C22C2×#6704311yescharacteristic
571C22C23×C22⋊D1111yescharacteristic
572C4—28no—
573C4—44no—
574C4—42no—
575C4—228no—
576C4—224no—
577C4—224no—
578C4—224no—
579C4—442no—
580C4—444no—
581C4C2×#6699218yes—
582C2—44no—
583C2#1307221718yesdirect product factor
584C2C22×#6699211yescharacteristic
585C2C2×#1062315311yescharacteristic
586C2C2×#1062315611yescharacteristic
587C2C2×#1062316211yescharacteristic
588C2C2×#1062336211yescharacteristic
589C2C2×#1062316311yescharacteristic
590C2C2×Q8×C22⋊D1111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2429
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66997C2semidirect
3. C22×Q8×Dic11C2semidirect
4. #13072217C2direct (N × H)
5. C2×#10622597C2semidirect
7. C2×#10622587C2semidirect
8. C2×#10622586C2semidirect
9. C2×#10622585C2semidirect
25. C2×Q8×Dic11C22semidirect
27. C2×#66997C22semidirect
45. #10622597C22semidirect
46. #10622587C22semidirect
47. #10622586C22semidirect
48. #10622585C22semidirect
83. C2×C22⋊Dic11Q8semidirect
180. C22⋊Dic11C2×Q8semidirect
400. C2×C11#2429semidirect
484. C11C2×#2429semidirect
583. C2#13072217direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669972
C22×#669772
C22×Q8×Dic112
#130722172
C2×#106225972
C2×#106225612
C2×#106225872
C2×#106225862
C2×#106225852
C2×#106225582
C2×C4×C22⋊Dic112
C22×C11×C22⋊Q82
C2×#242911