Finite Group Databasebeta

← C2×#13118438 #16030942

Subgroups — C2×#13118438 #16030942

Order 3328.

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×#88200C211yesmaximal, characteristic
2C22×#88200C211yesmaximal, characteristic
3C22×Q8×Dic13C211yesmaximal, characteristic, complemented
4#13118438C2116yesmaximal, direct product factor
5C2×#11718645C212yesmaximal, complemented
6C2×#11718655C212yesmaximal
7C2×#11718891C211yesmaximal, characteristic, complemented
8C2×#11718589C211yesmaximal, characteristic, complemented
9C2×#11718633C212yesmaximal, complemented
10C2×#11718651C212yesmaximal
11C2×C4×#6103C211yesmaximal, characteristic
12C22×C13×C4⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C23×Q8×C13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C2×C13×C4⋊Q8—28no—
17C2×C13×C4⋊Q8C2218yescomplemented
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2212yes—
20C22×C42×C13C2211yescharacteristic
21C2×#88200—28no—
22C2×#88200—28no—
23C2×#88200C2218yes—
24C2×#88200C2218yes—
25C2×Q8×Dic13—28no—
26C2×Q8×Dic13C2218yescomplemented
27C22×#6103C2212yes—
28C22×#6103C2212yes—
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×C4⋊Dic13C2212yes—
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×#6101C2212yes—
35C22×#6101C2212yes—
36C22×#6101C2212yes—
37C22×C4×Dic13C2212yes—
38C22×C4×Dic13C2211yescharacteristic
39#11718891C2218yescomplemented
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2211yescharacteristic
43C2×#88071C2212yes—
44C2×#88071C2211yescharacteristic
45#11718655C22116yes—
46#11718651C22116yes—
47#11718645C22116yescomplemented
48#11718633C22116yescomplemented
49C4×#6103C2218yes—
50#11718589C2218yescomplemented
51C24×D13C2311yescharacteristic
52C22×Q8×C13—24no—
53C22×Q8×C13—24no—
54C22×Q8×C13—24no—
55C22×Q8×C13—24no—
56C22×Q8×C13—24no—
57C22×Q8×C13D418yes—
58C22×Q8×C13C2314yes—
59C22×Q8×C13C2314yes—
60C23×C4×C13C2312yes—
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2312yes—
68C23×Dic13C2312yes—
69C23×Dic13C2311yescharacteristic
70C22×C4×D13—24no—
71C22×C4×D13—24no—
72C22×C4×D13—24no—
73C22×C4×D13C2314yes—
74C13×C4⋊Q8—232no—
75C2×C13×C4⋊C4—28no—
76C2×C13×C4⋊C4—28no—
77C2×C13×C4⋊C4C2318yes—
78C2×C13×C4⋊C4C2318yes—
79C2×C42×C13—24no—
80C2×C42×C13C2314yes—
81#88200—232no—
82#88200—232no—
83Q8×Dic13—232no—
84C2×#6103—28no—
85C2×#6103—24no—
86C2×#6103—28no—
87C2×#6103Q818yescomplemented
88C2×#6103C2318yes—
89C2×#6103C2318yes—
90C2×#6103C2314yes—
91C2×#6103C2314yes—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—28no—
94C2×C4⋊Dic13D418yes—
95C2×C4⋊Dic13C2318yes—
96C2×C4⋊Dic13C2314yes—
97C2×C4⋊Dic13C2314yes—
98C2×#6101—28no—
99C2×#6101—28no—
100C2×#6101—28no—
101C2×#6101C2318yes—
102C2×#6101C2318yes—
103C2×#6101C2318yes—
104C2×C4×Dic13—24no—
105C2×C4×Dic13—28no—
106C2×C4×Dic13C2314yes—
107C2×C4×Dic13C2318yes—
108#88071C2318yes—
109#88071C2314yes—
110#88071C2314yes—
111#88071C2318yes—
112#88071C2318yes—
113C2×#2429—131nomaximal, Sylow
114C24×C13C2411yescharacteristic
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13C2×Q814yes—
122C23×D13C2412yes—
123C2×Q8×C13—232no—
124C2×Q8×C13—28no—
125C2×Q8×C13—28no—
126C2×Q8×C13—28no—
127C2×Q8×C13—28no—
128C2×Q8×C13—28no—
129C2×Q8×C13—416no—
130C2×Q8×C13C2×D4116yes—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×D418yes—
142C22×C4×C13C2×D414yes—
143C22×C4×C13C2×Q814yes—
144C22×C4×C13#4114yes—
145C22×C4×C13#4114yes—
146C22×C4×C13C2414yes—
147C22×C4×C13C2414yes—
148C22×C4×C13C2412yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2412yes—
151C22×Dic13—22no—
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—24no—
164C22×Dic13C2×D418yes—
165C22×Dic13C2×Q814yes—
166C22×Dic13C2412yes—
167C22×Dic13C2414yes—
168C22×Dic13C2412yes—
169C22×Dic13C2414yes—
170C22×Dic13C2412yes—
171C2×C4×D13—28no—
172C2×C4×D13—28no—
173C2×C4×D13—28no—
174C2×C4×D13—416no—
175C13×C4⋊C4—216no—
176C13×C4⋊C4—216no—
177C42×C13—28no—
178#6103—216no—
179#6103—28no—
180#6103—216no—
181#6103C2×Q8116yescomplemented
182C4⋊Dic13—28no—
183C4⋊Dic13—216no—
184C4⋊Dic13C2×D4116yes—
185#6101—216no—
186#6101—216no—
187#6101—216no—
188C4×Dic13—28no—
189C4×Dic13—216no—
190C22×C4⋊Q8D1311yescharacteristic, complemented
191C22×C22⋊Q8—131no—
192C22×C22⋊Q8—131no—
193C22×C4×Q8—131no—
194#2429—1316no—
195C2×#398—132no—
196C2×#396—132no—
197C2×#391—131no—
198C2×#389—131no—
199C2×#389—132no—
200C2×#388—132no—
201C2×C4×C22⋊C4—131no—
202C23×C13C22×D412yes—
203C23×C13C22×D412yes—
204C23×C13C22×Q812yes—
205C23×C13C2×#4112yes—
206C23×C13C2×#4112yes—
207C23×C132−1+412yes—
208C23×C132−1+412yes—
209C23×C13C2511yescharacteristic
210C22×D13—28no—
211C22×D13—28no—
212C22×D13—28no—
213C22×D13—22no—
214C22×D13—22no—
215C22×D13—22no—
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—44no—
220C22×D13—44no—
221C22×D13—44no—
222C22×D13—44no—
223C22×D13C22×Q814yes—
224Q8×C13—232no—
225Q8×C13—416no—
226C2×C4×C13—216no—
227C2×C4×C13—28no—
228C2×C4×C13—28no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—24no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—24no—
238C2×C4×C13—48no—
239C2×C4×C13#121116yes—
240C2×C4×C13C22×D418yes—
241C2×C4×C13C22×D414yes—
242C2×C4×C13C22×D414yes—
243C2×C4×C13C22×Q814yes—
244C2×C4×C13C2×#4114yes—
245C2×C4×C13C2×#4114yes—
246C2×Dic13—216no—
247C2×Dic13—28no—
248C2×Dic13—22no—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—44no—
262C2×Dic13—44no—
263C2×Dic13—48no—
264C2×Dic13C22×D418yes—
265C2×Dic13C22×Q814yes—
266C4×D13—416no—
267C23×Q8C2×D1311yescharacteristic
268C23×Q8C2×D1311yescharacteristic
269C24×C4—131no—
270C2×C4⋊Q8—28no—
271C2×C4⋊Q8C2×D1318yescomplemented
272C2×C22⋊Q8—138no—
273C2×C22⋊Q8—138no—
274C2×C22⋊Q8—268no—
275C2×C22⋊Q8—268no—
276C2×C4×Q8—138no—
277C2×C4×Q8—268no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4C2×D1312yes—
285C22×C4⋊C4C2×D1312yes—
286C22×C22⋊C4—131no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C42—131no—
291C22×C42—132no—
292C22×C42C2×D1311yescharacteristic
293#398—1316no—
294#396—1316no—
295#391—138no—
296#389—1316no—
297#389—138no—
298#388—1316no—
299C4×C22⋊C4—138no—
300C2×#95—132no—
301C2×#95—131no—
302C2×#95—132no—
303C2×#95—131no—
304C2×#95—132no—
305C22×C13C2×#12114yes—
306C22×C13#53314yes—
307C22×C13#54114yes—
308C22×C13#54714yes—
309C22×C13#54814yes—
310C22×C13D4×Q814yes—
311C22×C13D4×Q814yes—
312C22×C13C23×D411yescharacteristic
313C22×C13C23×D411yescharacteristic
314C22×C13C23×Q811yescharacteristic
315C22×C13C22×#4111yescharacteristic
316C22×C13C22×#4111yescharacteristic
317C22×C13C2×2−1+411yescharacteristic
318C22×C13C2×2−1+411yescharacteristic
319C2×D13—24no—
320C2×D13—24no—
321C2×D13—24no—
322C2×D13—42no—
323C2×D13—416no—
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—42no—
327C4×C13—28no—
328C4×C13—24no—
329C4×C13—24no—
330C4×C13—44no—
331C4×C13C2×#12118yes—
332Dic13—28no—
333Dic13—24no—
334Dic13—42no—
335Dic13—42no—
336Dic13—44no—
337C25—131no—
338C22×Q8—24no—
339C22×Q8—24no—
340C22×Q8—24no—
341C22×Q8—24no—
342C22×Q8—24no—
343C22×Q8C22⋊D1318yes—
344C22×Q8C22×D1314yes—
345C22×Q8C22×D1314yes—
346C23×C4—132no—
347C23×C4—131no—
348C23×C4—132no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—134no—
352C23×C4—264no—
353C23×C4—264no—
354C23×C4—264no—
355C23×C4C22×D1312yes—
356C23×C4C22×D1311yescharacteristic
357C23×C4C22×D1311yescharacteristic
358C23×C4C22×D1312yes—
359C23×C4C22×D1311yescharacteristic
360C4⋊Q8—232no—
361C22⋊Q8—2632no—
362C22⋊Q8—2632no—
363C4×Q8—2632no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—138no—
367C2×C4⋊C4—134no—
368C2×C4⋊C4—138no—
369C2×C4⋊C4—138no—
370C2×C4⋊C4—138no—
371C2×C4⋊C4—134no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—268no—
374C2×C4⋊C4—268no—
375C2×C4⋊C4—268no—
376C2×C4⋊C4—268no—
377C2×C4⋊C4—264no—
378C2×C4⋊C4C22×D1318yes—
379C2×C4⋊C4C22×D1318yes—
380C2×C22⋊C4—138no—
381C2×C22⋊C4—134no—
382C2×C22⋊C4—138no—
383C2×C22⋊C4—138no—
384C2×C22⋊C4—134no—
385C2×C22⋊C4—268no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—268no—
388C2×C42—24no—
389C2×C42—134no—
390C2×C42—138no—
391C2×C42—268no—
392C2×C42—264no—
393C2×C42C22×D1314yes—
394#95—134no—
395#95—134no—
396#95—138no—
397#95—138no—
398#95—138no—
399C2×C13#242918yescomplemented
400C2×C13C22×#12111yescharacteristic
401C2×C13C2×#53311yescharacteristic
402C2×C13C2×#54111yescharacteristic
403C2×C13C2×#54711yescharacteristic
404C2×C13C2×#54811yescharacteristic
405C2×C13C2×D4×Q811yescharacteristic
406C2×C13C2×D4×Q811yescharacteristic
407D13—44no—
408C24—134no—
409C24—132no—
410C24—262no—
411C24—262no—
412C24—262no—
413C24—262no—
414C24—262no—
415C24—262no—
416C24C23×D1311yescharacteristic
417C2×Q8—232no—
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—416no—
424C2×Q8C2×C22⋊D13116yes—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—138no—
435C22×C4—134no—
436C22×C4—132no—
437C22×C4—134no—
438C22×C4—132no—
439C22×C4—134no—
440C22×C4—132no—
441C22×C4—262no—
442C22×C4—264no—
443C22×C4—264no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—264no—
450C22×C4—262no—
451C22×C4—264no—
452C22×C4—264no—
453C22×C4—262no—
454C22×C4—268no—
455C22×C4—268no—
456C22×C4—268no—
457C22×C4—5216no—
458C22×C4D4×D1314yes—
459C22×C4#612914yes—
460C22×C4Q8×D1314yes—
461C22×C4#613114yes—
462C22×C4C2×C22⋊D1318yes—
463C22×C4C2×C22⋊D1314yes—
464C22×C4C23×D1314yes—
465C22×C4C23×D1312yes—
466C22×C4C23×D1312yes—
467C22×C4C23×D1314yes—
468C22×C4C23×D1312yes—
469C4⋊C4—216no—
470C4⋊C4—216no—
471C4⋊C4—1316no—
472C4⋊C4—2616no—
473C4⋊C4—2616no—
474C4⋊C4—2616no—
475C4⋊C4—2616no—
476C4⋊C4—268no—
477C22⋊C4—1316no—
478C22⋊C4—2616no—
479C22⋊C4—268no—
480C22⋊C4—2616no—
481C42—28no—
482C42—2616no—
483C42—268no—
484C13C2×#242911yescharacteristic, complemented, Sylow
485C23—134no—
486C23—268no—
487C23—268no—
488C23—268no—
489C23—262no—
490C23—262no—
491C23—262no—
492C23—262no—
493C23—262no—
494C23—262no—
495C23—524no—
496C23—524no—
497C23—524no—
498C23—524no—
499C23C2×D4×D1312yes—
500C23C2×#612912yes—
501C23C2×Q8×D1312yes—
502C23C2×#613112yes—
503C23#8825412yes—
504C23#8825412yes—
505C23C22×C22⋊D1312yes—
506C23C24×D1311yescharacteristic
507Q8—232no—
508Q8—416no—
509C2×C4—216no—
510C2×C4—28no—
511C2×C4—28no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—48no—
522C2×C4—138no—
523C2×C4—134no—
524C2×C4—2616no—
525C2×C4—268no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—264no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—264no—
535C2×C4—262no—
536C2×C4—264no—
537C2×C4—264no—
538C2×C4—262no—
539C2×C4—524no—
540C2×C4—524no—
541C2×C4—528no—
542C2×C4—5216no—
543C2×C4#88193116yes—
544C2×C4C2×D4×D1314yes—
545C2×C4C2×#612914yes—
546C2×C4C2×Q8×D1314yes—
547C2×C4C2×#613114yes—
548C2×C4C22×C22⋊D1318yes—
549C2×C4C22×C22⋊D1314yes—
550C22—264no—
551C22—264no—
552C22—264no—
553C22—522no—
554C22—522no—
555C22—522no—
556C22—522no—
557C22—5216no—
558C22#1171943114yes—
559C22#1171943214yes—
560C22#1171943314yes—
561C22#1171943614yes—
562C22C2×#8819314yes—
563C22Q8×C22⋊D1314yes—
564C22#1171952214yes—
565C22C22×D4×D1311yescharacteristic
566C22C22×#612911yescharacteristic
567C22C22×Q8×D1311yescharacteristic
568C22C22×#613111yescharacteristic
569C22C2×#8825411yescharacteristic
570C22C2×#8825411yescharacteristic
571C22C23×C22⋊D1311yescharacteristic
572C4—24no—
573C4—24no—
574C4—28no—
575C4—44no—
576C4—268no—
577C4—264no—
578C4—522no—
579C4—524no—
580C4—522no—
581C4C2×#8819318yes—
582C2—524no—
583C2#1311843818yesdirect product factor
584C2C22×#8819311yescharacteristic
585C2C2×#1171943311yescharacteristic
586C2C2×#1171943611yescharacteristic
587C2C2×#1171943111yescharacteristic
588C2C2×#1171952211yescharacteristic
589C2C2×Q8×C22⋊D1311yescharacteristic
590C2C2×#1171943211yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C4⋊Q8C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC22×C4⋊Q8D13
hypocenterC13C2×#2429
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C22×Q8×Dic13C2semidirect
4. #13118438C2direct (N × H)
5. C2×#11718645C2semidirect
7. C2×#11718891C2semidirect
8. C2×#11718589C2semidirect
9. C2×#11718633C2semidirect
12. C22×C13×C4⋊Q8C2semidirect
17. C2×C13×C4⋊Q8C22semidirect
26. C2×Q8×Dic13C22semidirect
39. #11718891C22semidirect
47. #11718645C22semidirect
48. #11718633C22semidirect
50. #11718589C22semidirect
87. C2×#6103Q8semidirect
181. #6103C2×Q8semidirect
190. C22×C4⋊Q8D13semidirect
271. C2×C4⋊Q8C2×D13semidirect
399. C2×C13#2429semidirect
484. C13C2×#2429semidirect
583. C2#13118438direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×Q8×Dic132
#131184382
C2×#117186452
C2×#117186552
C2×#117188912
C2×#117185892
C2×#117186332
C2×#117186512
C2×C4×#61032
C22×C13×C4⋊Q82
C2×#242913