Finite Group Databasebeta

← #15618796

Subgroups — #15618796

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic
2#13077717C213yesmaximal, complemented
3#13077714C213yesmaximal, complemented
4#13077713C213yesmaximal, complemented
5#13077712C213yesmaximal, complemented
6#13077704C211yesmaximal, characteristic, complemented
7#13077697C211yesmaximal, characteristic, complemented
8#13077695C211yesmaximal, characteristic, complemented
9Q8×#4313C211yesmaximal, characteristic, complemented
10#13077564C213yesmaximal, complemented
11#13077547C213yesmaximal, complemented
12C8×Q8×D11C211yesmaximal, characteristic, complemented
13#13077283C213yesmaximal
14#13077255C213yesmaximal
15C11×#2984C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17Q8×C22⋊D11C411yescharacteristic
18Q8×C22⋊D11C411yescharacteristic
19#10623110C413yes—
20#10623109C2213yes—
21#10623109C2213yes—
22Q8×D44C411yescharacteristic
23C4×Q8×D11C2211yescharacteristic
24C4×Q8×D11C2211yescharacteristic
25#10623098C413yes—
26Q8×Dic22C411yescharacteristic
27#10623042C413yes—
28#10623042C413yes—
29C4×#4339C2213yes—
30#10623001C2213yes—
31C11×#446C2213yes—
32C11×#446C2213yes—
33C8×Q8×C11C2211yescharacteristic
34C8×Q8×C11C2211yescharacteristic
35C11×#432C2213yes—
36C11×#431C2213yes—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2213yes—
39Q8×C11⋊C8C2213yes—
40Q8×C11⋊C8C2211yescharacteristic
41#10622538C2213yes—
42#10622538C2213yes—
43#10622453C2213yes—
44#10622453C2213yes—
45#10622452C2213yes—
46#10622452C2213yes—
47#10622450C2213yes—
48#10622448C2213yes—
49#10622446C2213yes—
50D11×C4⋊C8C2213yes—
51#10622444C2213yes—
52#10622444C2216yes—
53#10622444C2213yes—
54#10622443C2213yes—
55#10622443C2213yes—
56#10622443C2216yes—
57#10622340C2211yescharacteristic
58#10622340C2213yes—
59#10622333C2213yes—
60#10622333C2213yes—
61#10622333C2216yes—
62#10622322C2216yes—
63#10622321C2216yes—
64#10622314C2216yes—
65#10622314C2216yes—
66C4×#4313C2213yes—
67#10622298C2213yes—
68#10622298C2213yes—
69C4×C8×D11C2213yes—
70#10622292C2213yes—
71#10622292C2213yes—
72C8×Dic22C2213yes—
73C8×Dic22C2213yes—
74C22×Q8×C11C2×C411yescharacteristic
75C2×Q8×D11C2×C411yescharacteristic
76C2×Q8×D11C2×C411yescharacteristic
77C2×#4339C2311yescharacteristic
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2×C413yes—
80C4×Q8×C11C2311yescharacteristic
81C4×Q8×C11C2313yes—
82C2×C11×C4⋊C4C2×C413yes—
83C2×C42×C11C2313yes—
84#66999C2×C413yes—
85#66999C2×C413yes—
86Q8×Dic11C2×C411yescharacteristic
87Q8×Dic11C2×C411yescharacteristic
88#66997C2×C413yes—
89#66997C2×C413yes—
90C4×C22⋊D11C2×C413yes—
91C4×C22⋊D11C2×C413yes—
92C4×C22⋊D11C2×C413yes—
93C4×C22⋊D11C2×C413yes—
94#66979C2313yes—
95#66977C2×C416yes—
96#66977C2×C413yes—
97#66977C2×C413yes—
98C2×#4313C2311yescharacteristic
99C2×#4313C2313yes—
100C2×C8×D11C2311yescharacteristic
101C2×C8×D11C2313yes—
102#66950C2×C413yes—
103#66950C2×C413yes—
104#66949C2×C416yes—
105#66949C2×C416yes—
106C4⋊C4×D11C2×C413yes—
107C4⋊C4×D11C2×C413yes—
108#66942C2×C416yes—
109#66942C2×C416yes—
110#66941C2×C413yes—
111#66941C2×C413yes—
112#66940C2×C413yes—
113#66940C2×C413yes—
114C4×D44C2×C413yes—
115C4×D44C2×C413yes—
116#66925C2313yes—
117#66925C2313yes—
118C42×D11C2313yes—
119C42×D11C2313yes—
120#66923C2×C416yes—
121#66922C2×C413yes—
122#66922C2×C413yes—
123C4×Dic22C2×C413yes—
124C4×Dic22C2×C413yes—
125C4×Dic22C2313yes—
126C4×Dic22C2313yes—
127C4×Dic22C2316yes—
128C11×C4⋊C8C2313yes—
129C11×C4⋊C8C2313yes—
130C11×C4⋊C8C2313yes—
131C11×C4⋊C8C2313yes—
132C11×C22⋊C8C2311yescharacteristic
133C11×C22⋊C8C2313yes—
134C11×#97C2316yes—
135C4×C8×C11C2313yes—
136C4×C8×C11C2313yes—
137C22⋊(C11⋊C8)C2311yescharacteristic
138C22⋊(C11⋊C8)C2313yes—
139(C2×D11)⋊C8C2311yescharacteristic
140(C2×D11)⋊C8C2311yescharacteristic
141(C2×D11)⋊C8C2313yes—
142(C2×D11)⋊C8C2313yes—
143#66879C2313yes—
144#66879C2316yes—
145#66879C2313yes—
146Dic11⋊C8C2313yes—
147Dic11⋊C8C2316yes—
148Dic11⋊C8C2313yes—
149Dic11⋊C8C2316yes—
150Dic11⋊C8C2313yes—
151Dic11⋊C8C2313yes—
152C8×Dic11C2313yes—
153C8×Dic11C2316yes—
154C8×Dic11C2313yes—
155C4⋊(C11⋊C8)C2313yes—
156C4⋊(C11⋊C8)C2313yes—
157C4⋊(C11⋊C8)C2313yes—
158C4⋊(C11⋊C8)C2313yes—
159C4×C11⋊C8C2313yes—
160C4×C11⋊C8C2313yes—
161C4×C11⋊C8C2316yes—
162#60253—111nomaximal, Sylow
163C2×Q8×C11—24no—
164C2×Q8×C11C22×C413yes—
165C2×Q8×C11C22×C411yescharacteristic
166C22×C4×C11C22×C413yes—
167C22×C4×C11C22×C413yes—
168C22×C4×C11C2411yescharacteristic
169C2×C22⋊D11C22×C411yescharacteristic
170C2×C22⋊D11C22×C411yescharacteristic
171Q8×D11—24no—
172Q8×D11—24no—
173#4339—22no—
174#4339—22no—
175C2×D44C22×C411yescharacteristic
176C2×C4×D11C22×C413yes—
177C2×C4×D11C22×C413yes—
178C2×C4×D11C22×C413yes—
179C2×C4×D11C22×C413yes—
180C2×C4×D11C2411yescharacteristic
181C2×C4×D11C2411yescharacteristic
182C2×Dic22C22×C411yescharacteristic
183C2×Dic22C22×C413yes—
184C2×Dic22C22×C413yes—
185C2×Dic22C22×C416yes—
186C2×C8×C11C2411yescharacteristic
187C2×C8×C11C2413yes—
188C2×C8×C11C2413yes—
189C2×C8×C11C2411yescharacteristic
190C11×C4⋊C4C22×C413yes—
191C11×C4⋊C4C22×C413yes—
192C11×C4⋊C4C22×C416yes—
193C42×C11C22×C413yes—
194C42×C11C22×C413yes—
195C42×C11C2413yes—
196C42×C11C2413yes—
197C22⋊Dic11C22×C413yes—
198C22⋊Dic11C22×C413yes—
199(C2×D11)⋊C4C22×C413yes—
200(C2×D11)⋊C4C22×C413yes—
201(C2×D11)⋊C4C22×C413yes—
202(C2×D11)⋊C4C22×C413yes—
203C4⋊Dic11C22×C413yes—
204C4⋊Dic11C22×C413yes—
205C4⋊Dic11C22×C413yes—
206C4⋊Dic11C22×C413yes—
207C4⋊Dic11C22×C416yes—
208Dic11⋊C4C22×C413yes—
209Dic11⋊C4C22×C413yes—
210Dic11⋊C4C22×C413yes—
211Dic11⋊C4C22×C413yes—
212Dic11⋊C4C22×C416yes—
213Dic11⋊C4C22×C416yes—
214Dic11⋊C4C22×C416yes—
215Dic11⋊C4C22×C416yes—
216C4×Dic11C22×C413yes—
217C4×Dic11C22×C413yes—
218C4×Dic11C22×C413yes—
219C4×Dic11C22×C413yes—
220C4×Dic11C2413yes—
221C4×Dic11C2413yes—
222C2×C11⋊C8C2411yescharacteristic
223C2×C11⋊C8C2413yes—
224C2×C11⋊C8C2411yescharacteristic
225C2×C11⋊C8C2413yes—
226#4313—22no—
227#4313—26no—
228C8×D11—26no—
229C8×D11—22no—
230Q8×#41—111no—
231#2986—113no—
232#2986—113no—
233#2985—113no—
234#2985—113no—
235#2984—111no—
236#2984D1111yescharacteristic, complemented
237#2982—111no—
238#2982—111no—
239Q8×M16—111no—
240#2962—113no—
241#2960—113no—
242C2×C8×Q8—111no—
243#2925—113no—
244#2922—113no—
245C23×C11C23×C411yescharacteristic
246C22×D11C23×C411yescharacteristic
247C22×D11C23×C411yescharacteristic
248Q8×C11—26no—
249Q8×C11#13114yes—
250C2×C4×C11—26no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—43no—
254C2×C4×C11C23×C413yes—
255C2×C4×C11C23×C413yes—
256C2×C4×C11C23×C413yes—
257C2×C4×C11C23×C411yescharacteristic
258C2×C4×C11C23×C413yes—
259C2×C4×C11C2511yescharacteristic
260C22⋊D11—22no—
261C22⋊D11—22no—
262C2×Dic11C23×C411yescharacteristic
263C2×Dic11C23×C413yes—
264C2×Dic11C23×C413yes—
265C2×Dic11C23×C413yes—
266C2×Dic11C23×C413yes—
267C2×Dic11C23×C411yescharacteristic
268D44—22no—
269C4×D11—26no—
270C4×D11—26no—
271C4×D11—21no—
272C4×D11—21no—
273C4×D11—43no—
274C4×D11—43no—
275C4×D112−1+412yes—
276C4×D112−1+412yes—
277Dic22—26no—
278Dic22—26no—
279Dic22—22no—
280Dic22—46no—
281C8×C11—21no—
282C8×C11—23no—
283C8×C11—23no—
284C8×C11—21no—
285C11⋊C8—23no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—23no—
289Q82—111no—
290#557—113no—
291#554—113no—
292#554—113no—
293#554—113no—
294D4×Q8—111no—
295D4×Q8—111no—
296D4×Q8—111no—
297#533—113no—
298#533—113no—
299#533—113no—
300C4×#41—113no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8C2×D1111yescharacteristic
304#446—113no—
305#446—116no—
306#446—113no—
307#446—116no—
308#446—116no—
309#446—113no—
310#446—113no—
311#446C2×D1113yes—
312#446C2×D1113yes—
313C8×Q8—111no—
314C8×Q8—113no—
315C8×Q8—113no—
316C8×Q8—111no—
317C8×Q8—113no—
318C8×Q8—113no—
319C8×Q8—116no—
320C8×Q8—113no—
321C8×Q8—113no—
322C8×Q8C2×D1111yescharacteristic
323C8×Q8C2×D1111yescharacteristic
324#433—113no—
325#433—113no—
326#433—113no—
327#433—113no—
328#433—116no—
329#433—116no—
330#432—113no—
331#432C2×D1113yes—
332#431—113no—
333#431—113no—
334#431—113no—
335#431—113no—
336#431—113no—
337#431C2×D1113yes—
338#424—113no—
339#424—113no—
340#423—113no—
341C2×C4⋊C8—113no—
342#408—111no—
343#408—113no—
344#405—116no—
345C4×M16—113no—
346C2×C4×C8—113no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11C24×C411yescharacteristic
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—21no—
355C2×D11—21no—
356C2×D11#51912yes—
357C4×C11—21no—
358C4×C11—23no—
359C4×C11—23no—
360C4×C11—23no—
361C4×C11C2×#13116yes—
362C4×C11C2×2−1+411yescharacteristic
363C4×C11C2×2−1+411yescharacteristic
364Dic11—21no—
365Dic11—23no—
366Dic11—23no—
367Dic11—23no—
368Dic11—23no—
369Dic11#51912yes—
370C2×#41—111no—
371C22×Q8—111no—
372C22×Q8—111no—
373C22×Q8C4×D1111yescharacteristic
374C2×M16—111no—
375C2×M16—113no—
376C22×C8—111no—
377C22×C8—113no—
378C4⋊Q8—113no—
379C4⋊Q8—113no—
380C4⋊Q8—113no—
381C4⋊Q8—113no—
382C4⋊Q8—113no—
383C4⋊Q8—113no—
384#125—116no—
385#125—116no—
386#125—116no—
387C22⋊Q8—113no—
388C22⋊Q8—113no—
389C22⋊Q8—113no—
390C22⋊Q8—113no—
391C22⋊Q8—116no—
392C22⋊Q8—113no—
393C22⋊Q8—113no—
394C22⋊Q8—116no—
395C22⋊Q8—116no—
396C4×Q8—111no—
397C4×Q8—111no—
398C4×Q8—113no—
399C4×Q8—113no—
400C4×Q8—113no—
401C4×Q8—113no—
402C4×Q8—113no—
403C4×Q8—113no—
404C4×Q8—116no—
405C4×Q8C4×D1111yescharacteristic
406C4×Q8C4×D1113yes—
407C4×Q8C22×D1111yescharacteristic
408C4×Q8C22×D1113yes—
409C4×D4—113no—
410C4×D4—113no—
411C4×D4—113no—
412C4×D4—113no—
413C4×D4—113no—
414C4×D4—113no—
415#117—113no—
416#117—113no—
417#117—113no—
418C2×C4⋊C4—113no—
419C2×C4⋊C4—113no—
420C2×C4⋊C4C4×D1113yes—
421C2×C42—113no—
422C2×C42—113no—
423C2×C42C22×D1113yes—
424C4⋊C8—116no—
425C4⋊C8—116no—
426C4⋊C8—113no—
427C4⋊C8—113no—
428C4⋊C8—113no—
429C4⋊C8—113no—
430C4⋊C8—113no—
431C4⋊C8—113no—
432C4⋊C8—113no—
433C4⋊C8—113no—
434C4⋊C8C22×D1113yes—
435C4⋊C8C22×D1113yes—
436C4⋊C8C22×D1113yes—
437C4⋊C8C22×D1113yes—
438C22⋊C8—111no—
439C22⋊C8—113no—
440C22⋊C8—113no—
441C22⋊C8—111no—
442C22⋊C8—111no—
443C22⋊C8—113no—
444C22⋊C8C22×D1111yescharacteristic
445C22⋊C8C22×D1113yes—
446#97—113no—
447#97—113no—
448#97—116no—
449#97C22×D1116yes—
450C4×C8—113no—
451C4×C8—113no—
452C4×C8—116no—
453C4×C8—113no—
454C4×C8—113no—
455C4×C8—116no—
456C4×C8C22×D1113yes—
457C4×C8C22×D1113yes—
458C2×C11—41no—
459C2×C11C2×#51911yescharacteristic
460C2×C11C22×#13111yescharacteristic
461C2×C11#357311yescharacteristic
462D11—22no—
463D11—41no—
464#41—222no—
465#41—222no—
466C2×Q8—24no—
467C2×Q8—111no—
468C2×Q8—113no—
469C2×Q8—113no—
470C2×Q8—116no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8C2×C4×D1113yes—
474C2×Q8C2×C4×D1111yescharacteristic
475C2×D4—111no—
476C2×D4—111no—
477C2×D4—111no—
478C22×C4—111no—
479C22×C4—113no—
480C22×C4—113no—
481C22×C4—111no—
482C22×C4—113no—
483C22×C4—113no—
484C22×C4C2×C4×D1113yes—
485C22×C4C2×C4×D1113yes—
486C22×C4C23×D1111yescharacteristic
487M16—222no—
488M16—226no—
489C2×C8—113no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—113no—
493C2×C8—226no—
494C2×C8—222no—
495C2×C8C23×D1111yescharacteristic
496C2×C8C23×D1113yes—
497C2×C8C23×D1113yes—
498C2×C8C23×D1111yescharacteristic
499C4⋊C4—116no—
500C4⋊C4—116no—
501C4⋊C4—113no—
502C4⋊C4—113no—
503C4⋊C4—113no—
504C4⋊C4—113no—
505C4⋊C4—113no—
506C4⋊C4—113no—
507C4⋊C4—113no—
508C4⋊C4—113no—
509C4⋊C4—116no—
510C4⋊C4—116no—
511C4⋊C4—116no—
512C4⋊C4C2×C4×D1113yes—
513C4⋊C4C2×C4×D1116yes—
514C4⋊C4C2×C4×D1113yes—
515C22⋊C4—113no—
516C22⋊C4—113no—
517C22⋊C4—113no—
518C22⋊C4—113no—
519C22⋊C4—113no—
520C22⋊C4—113no—
521C42—113no—
522C42—113no—
523C42—113no—
524C42—113no—
525C42—113no—
526C42—113no—
527C42C2×C4×D1113yes—
528C42C2×C4×D1113yes—
529C42C23×D1113yes—
530C42C23×D1113yes—
531C11#6025311yescharacteristic, complemented, Sylow
532C23—111no—
533C23—111no—
534C23C22×C4×D1111yescharacteristic
535Q8—26no—
536Q8—222no—
537Q8—226no—
538Q8—226no—
539Q8—446no—
540Q8#6696014yes—
541D4—222no—
542D4—222no—
543D4—222no—
544C2×C4—26no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—43no—
548C2×C4—111no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—111no—
552C2×C4—113no—
553C2×C4—113no—
554C2×C4—113no—
555C2×C4—113no—
556C2×C4—226no—
557C2×C4—226no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—443no—
561C2×C4—443no—
562C2×C4C22×C4×D1113yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C22×C4×D1113yes—
565C2×C4C22×C4×D1113yes—
566C2×C4C22×C4×D1113yes—
567C2×C4C24×D1111yescharacteristic
568C8—21no—
569C8—23no—
570C8—23no—
571C8—21no—
572C8—223no—
573C8—221no—
574C8—221no—
575C8—223no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—112no—
580C22—221no—
581C22—221no—
582C22—221no—
583C22—221no—
584C22—221no—
585C22C23×C4×D1111yescharacteristic
586C4—23no—
587C4—23no—
588C4—23no—
589C4—21no—
590C4—112no—
591C4—223no—
592C4—223no—
593C4—223no—
594C4—223no—
595C4—221no—
596C4C2×#6696016yes—
597C4D11×2−1+411yescharacteristic
598C4D11×2−1+411yescharacteristic
599C2—41no—
600C2—222no—
601C2—441no—
602C2D11×#51911yescharacteristic
603C2C22×#6696011yescharacteristic
604C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2984C2
prime radicalC2×#4339C23
cosocleC2×C4×C11C25
hypercenter#2984D11
hypocenterC11#60253
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2984

Complements

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

NH ≅ G/Ntype
2. #13077717C2semidirect
3. #13077714C2semidirect
4. #13077713C2semidirect
5. #13077712C2semidirect
6. #13077704C2semidirect
7. #13077697C2semidirect
8. #13077695C2semidirect
9. Q8×#4313C2semidirect
10. #13077564C2semidirect
11. #13077547C2semidirect
12. C8×Q8×D11C2semidirect
15. C11×#2984C2semidirect
236. #2984D11semidirect
531. C11#60253semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130777172
#130777142
#130777132
#130777122
#130777042
#130776972
#130776952
Q8×#43132
#130775642
#130775472
C8×Q8×D112
#130772832
#130772552
C11×#29842
#6025311